Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals
Search results

Search: All articles in the CMB digital archive with keyword operators

 Expand all        Collapse all Results 1 - 25 of 37

1. CMB Online first

Xu, Xu; Zhu, Laiyi
 Rational function operators from Poisson integrals In this paper, we construct two classes of rational function operators by using the Poisson integrals of the function on the whole real axis. The convergence rates of the uniform and mean approximation of such rational function operators on the whole real axis are studied. Keywords:rational function operators, Poisson integrals, convergence rate, uniform approximation, mean approximationCategories:41A20, 41A25, 41A35

2. CMB Online first

Liu, Feng; Wu, Huoxiong
 Endpoint Regularity of Multisublinear Fractional Maximal Functions In this paper we investigate the endpoint regularity properties of the multisublinear fractional maximal operators, which include the multisublinear Hardy-Littlewood maximal operator. We obtain some new bounds for the derivative of the one-dimensional multisublinear fractional maximal operators acting on vector-valued function $\vec{f}=(f_1,\dots,f_m)$ with all $f_j$ being $BV$-functions. Keywords:multisublinear fractional maximal operators, Sobolev spaces, bounded variationCategories:42B25, 46E35

3. CMB 2016 (vol 59 pp. 497)

De Carli, Laura; Samad, Gohin Shaikh
 One-parameter Groups of Operators and Discrete Hilbert Transforms We show that the discrete Hilbert transform and the discrete Kak-Hilbert transform are infinitesimal generator of one-parameter groups of operators in $\ell^2$. Keywords:discrete Hilbert transform, groups of operators, isometriesCategories:42A45, 42A50, 41A44

4. CMB 2015 (vol 58 pp. 241)

Botelho, Fernanda
 Isometries and Hermitian Operators on Zygmund Spaces In this paper we characterize the isometries of subspaces of the little Zygmund space. We show that the isometries of these spaces are surjective and represented as integral operators. We also show that all hermitian operators on these settings are bounded. Keywords:Zygmund spaces, the little Zygmund space, Hermitian operators, surjective linear isometries, generators of one-parameter groups of surjective isometriesCategories:46E15, 47B15, 47B38

5. CMB 2014 (vol 58 pp. 51)

De Nitties, Giuseppe; Schulz-Baldes, Hermann
 Spectral Flows of Dilations of Fredholm Operators Given an essentially unitary contraction and an arbitrary unitary dilation of it, there is a naturally associated spectral flow which is shown to be equal to the index of the operator. This result is interpreted in terms of the $K$-theory of an associated mapping cone. It is then extended to connect $\mathbb{Z}_2$ indices of odd symmetric Fredholm operators to a $\mathbb{Z}_2$-valued spectral flow. Keywords:spectral flow, Fredholm operators, Z2 indicesCategories:19K56, 46L80

6. CMB 2014 (vol 57 pp. 834)

Koh, Doowon
 Restriction Operators Acting on Radial Functions on Vector Spaces Over Finite Fields We study $L^p-L^r$ restriction estimates for algebraic varieties $V$ in the case when restriction operators act on radial functions in the finite field setting. We show that if the varieties $V$ lie in odd dimensional vector spaces over finite fields, then the conjectured restriction estimates are possible for all radial test functions. In addition, assuming that the varieties $V$ are defined in even dimensional spaces and have few intersection points with the sphere of zero radius, we also obtain the conjectured exponents for all radial test functions. Keywords:finite fields, radial functions, restriction operatorsCategories:42B05, 43A32, 43A15

7. CMB 2013 (vol 57 pp. 546)

 Compact Operators in Regular LCQ Groups We show that a regular locally compact quantum group $\mathbb{G}$ is discrete if and only if $\mathcal{L}^{\infty}(\mathbb{G})$ contains non-zero compact operators on $\mathcal{L}^{2}(\mathbb{G})$. As a corollary we classify all discrete quantum groups among regular locally compact quantum groups $\mathbb{G}$ where $\mathcal{L}^{1}(\mathbb{G})$ has the Radon--Nikodym property. Keywords:locally compact quantum groups, regularity, compact operatorsCategory:46L89

8. CMB 2012 (vol 57 pp. 25)

Bourin, Jean-Christophe; Harada, Tetsuo; Lee, Eun-Young
 Subadditivity Inequalities for Compact Operators Some subadditivity inequalities for matrices and concave functions also hold for Hilbert space operators, but (unfortunately!) with an additional $\varepsilon$ term. It seems not possible to erase this residual term. However, in case of compact operators we show that the $\varepsilon$ term is unnecessary. Further, these inequalities are strict in a certain sense when some natural assumptions are satisfied. The discussion also stresses on matrices and their compressions and several open questions or conjectures are considered, both in the matrix and operator settings. Keywords:concave or convex function, Hilbert space, unitary orbits, compact operators, compressions, matrix inequalitiesCategories:47A63, 15A45

9. CMB 2011 (vol 56 pp. 229)

Arvanitidis, Athanasios G.; Siskakis, Aristomenis G.
 CesÃ ro Operators on the Hardy Spaces of the Half-Plane In this article we study the CesÃ ro operator $$\mathcal{C}(f)(z)=\frac{1}{z}\int_{0}^{z}f(\zeta)\,d\zeta,$$ and its companion operator $\mathcal{T}$ on Hardy spaces of the upper half plane. We identify $\mathcal{C}$ and $\mathcal{T}$ as resolvents for appropriate semigroups of composition operators and we find the norm and the spectrum in each case. The relation of $\mathcal{C}$ and $\mathcal{T}$ with the corresponding Ces\`{a}ro operators on Lebesgue spaces $L^p(\mathbb R)$ of the boundary line is also discussed. Keywords:CesÃ ro operators, Hardy spaces, semigroups, composition operatorsCategories:47B38, 30H10, 47D03

10. CMB 2011 (vol 56 pp. 65)

Ghenciu, Ioana
 The Uncomplemented Subspace $\mathbf K(X,Y)$ A vector measure result is used to study the complementation of the space $K(X,Y)$ of compact operators in the spaces $W(X,Y)$ of weakly compact operators, $CC(X,Y)$ of completely continuous operators, and $U(X,Y)$ of unconditionally converging operators. Results of Kalton and Emmanuele concerning the complementation of $K(X,Y)$ in $L(X,Y)$ and in $W(X,Y)$ are generalized. The containment of $c_0$ and $\ell_\infty$ in spaces of operators is also studied. Keywords:compact operators, weakly compact operators, uncomplemented subspaces of operatorsCategories:46B20, 46B28

11. CMB 2011 (vol 55 pp. 449)

Bahreini, Manijeh; Bator, Elizabeth; Ghenciu, Ioana
 Complemented Subspaces of Linear Bounded Operators We study the complementation of the space $W(X,Y)$ of weakly compact operators, the space $K(X,Y)$ of compact operators, the space $U(X,Y)$ of unconditionally converging operators, and the space $CC(X,Y)$ of completely continuous operators in the space $L(X,Y)$ of bounded linear operators from $X$ to $Y$. Feder proved that if $X$ is infinite-dimensional and $c_0 \hookrightarrow Y$, then $K(X,Y)$ is uncomplemented in $L(X,Y)$. Emmanuele and John showed that if $c_0 \hookrightarrow K(X,Y)$, then $K(X,Y)$ is uncomplemented in $L(X,Y)$. Bator and Lewis showed that if $X$ is not a Grothendieck space and $c_0 \hookrightarrow Y$, then $W(X,Y)$ is uncomplemented in $L(X,Y)$. In this paper, classical results of Kalton and separably determined operator ideals with property $(*)$ are used to obtain complementation results that yield these theorems as corollaries. Keywords:spaces of operators, complemented subspaces, compact operators, weakly compact operators, completely continuous operatorsCategories:46B20, 46B28

12. CMB 2011 (vol 55 pp. 579)

Ndogmo, J. C.
 Casimir Operators and Nilpotent Radicals It is shown that a Lie algebra having a nilpotent radical has a fundamental set of invariants consisting of Casimir operators. A different proof is given in the well known special case of an abelian radical. A result relating the number of invariants to the dimension of the Cartan subalgebra is also established. Keywords:nilpotent radical, Casimir operators, algebraic Lie algebras, Cartan subalgebras, number of invariantsCategories:16W25, 17B45, 16S30

13. CMB 2011 (vol 55 pp. 548)

Lewis, Paul; Schulle, Polly
 Non-complemented Spaces of Operators, Vector Measures, and $c_o$ The Banach spaces $L(X, Y)$, $K(X, Y)$, $L_{w^*}(X^*, Y)$, and $K_{w^*}(X^*, Y)$ are studied to determine when they contain the classical Banach spaces $c_o$ or $\ell_\infty$. The complementation of the Banach space $K(X, Y)$ in $L(X, Y)$ is discussed as well as what impact this complementation has on the embedding of $c_o$ or $\ell_\infty$ in $K(X, Y)$ or $L(X, Y)$. Results of Kalton, Feder, and Emmanuele concerning the complementation of $K(X, Y)$ in $L(X, Y)$ are generalized. Results concerning the complementation of the Banach space $K_{w^*}(X^*, Y)$ in $L_{w^*}(X^*, Y)$ are also explored as well as how that complementation affects the embedding of $c_o$ or $\ell_\infty$ in $K_{w^*}(X^*, Y)$ or $L_{w^*}(X^*, Y)$. The $\ell_p$ spaces for $1 = p < \infty$ are studied to determine when the space of compact operators from one $\ell_p$ space to another contains $c_o$. The paper contains a new result which classifies these spaces of operators. A new result using vector measures is given to provide more efficient proofs of theorems by Kalton, Feder, Emmanuele, Emmanuele and John, and Bator and Lewis. Keywords:spaces of operators, compact operators, complemented subspaces, $w^*-w$-compact operatorsCategory:46B20

14. CMB 2011 (vol 55 pp. 297)

Glasner, Eli
 The Group $\operatorname{Aut}(\mu)$ is Roelcke Precompact Following a similar result of Uspenskij on the unitary group of a separable Hilbert space, we show that, with respect to the lower (or Roelcke) uniform structure, the Polish group $G= \operatorname{Aut}(\mu)$ of automorphisms of an atomless standard Borel probability space $(X,\mu)$ is precompact. We identify the corresponding compactification as the space of Markov operators on $L_2(\mu)$ and deduce that the algebra of right and left uniformly continuous functions, the algebra of weakly almost periodic functions, and the algebra of Hilbert functions on $G$, i.e., functions on $G$ arising from unitary representations, all coincide. Again following Uspenskij, we also conclude that $G$ is totally minimal. Keywords:Roelcke precompact, unitary group, measure preserving transformations, Markov operators, weakly almost periodic functionsCategories:54H11, 22A05, 37B05, 54H20

15. CMB 2011 (vol 54 pp. 456)

Gustafson, Karl
 On Operator Sum and Product Adjoints and Closures We comment on domain conditions that regulate when the adjoint of the sum or product of two unbounded operators is the sum or product of their adjoints, and related closure issues. The quantum mechanical problem PHP essentially selfadjoint for unbounded Hamiltonians is addressed, with new results. Keywords:unbounded operators, adjoints of sums and products, quantum mechanicsCategory:47A05

16. CMB 2011 (vol 55 pp. 339)

Loring, Terry A.
 From Matrix to Operator Inequalities We generalize LÃ¶wner's method for proving that matrix monotone functions are operator monotone. The relation $x\leq y$ on bounded operators is our model for a definition of $C^{*}$-relations being residually finite dimensional. Our main result is a meta-theorem about theorems involving relations on bounded operators. If we can show there are residually finite dimensional relations involved and verify a technical condition, then such a theorem will follow from its restriction to matrices. Applications are shown regarding norms of exponentials, the norms of commutators, and "positive" noncommutative $*$-polynomials. Keywords:$C*$-algebras, matrices, bounded operators, relations, operator norm, order, commutator, exponential, residually finite dimensionalCategories:46L05, 47B99

17. CMB 2011 (vol 55 pp. 441)

Zorboska, Nina
 Univalently Induced, Closed Range, Composition Operators on the Bloch-type Spaces While there is a large variety of univalently induced closed range composition operators on the Bloch space, we show that the only univalently induced, closed range, composition operators on the Bloch-type spaces $B^{\alpha}$ with $\alpha \ne 1$ are the ones induced by a disc automorphism. Keywords:composition operators, Bloch-type spaces, closed range, univalentCategories:47B35, 32A18

18. CMB 2011 (vol 54 pp. 498)

 On the Adjoint and the Closure of the Sum of Two Unbounded Operators We prove, under some conditions on the domains, that the adjoint of the sum of two unbounded operators is the sum of their adjoints in both Hilbert and Banach space settings. A similar result about the closure of operators is also proved. Some interesting consequences and examples "spice up" the paper. Keywords:unbounded operators, sum and products of operators, Hilbert and Banach adjoints, self-adjoint operators, closed operators, closure of operatorsCategory:47A05

19. CMB 2011 (vol 54 pp. 716)

Okassa, Eugène
 Symplectic Lie-Rinehart-Jacobi Algebras and Contact Manifolds We give a characterization of contact manifolds in terms of symplectic Lie-Rinehart-Jacobi algebras. We also give a sufficient condition for a Jacobi manifold to be a contact manifold. Keywords:Lie-Rinehart algebras, differential operators, Jacobi manifolds, symplectic manifolds, contact manifoldsCategories:13N05, 53D05, 53D10

20. CMB 2010 (vol 54 pp. 141)

Kim, Sang Og; Park, Choonkil
 Linear Maps on $C^*$-Algebras Preserving the Set of Operators that are Invertible in $\mathcal{A}/\mathcal{I}$ For $C^*$-algebras $\mathcal{A}$ of real rank zero, we describe linear maps $\phi$ on $\mathcal{A}$ that are surjective up to ideals $\mathcal{I}$, and $\pi(A)$ is invertible in $\mathcal{A}/\mathcal{I}$ if and only if $\pi(\phi(A))$ is invertible in $\mathcal{A}/\mathcal{I}$, where $A\in\mathcal{A}$ and $\pi:\mathcal{A}\to\mathcal{A}/\mathcal{I}$ is the quotient map. We also consider similar linear maps preserving zero products on the Calkin algebra. Keywords:preservers, Jordan automorphisms, invertible operators, zero productsCategories:47B48, 47A10, 46H10

21. CMB 2010 (vol 53 pp. 327)

Luor, Dah-Chin
 Multidimensional Exponential Inequalities with Weights We establish sufficient conditions on the weight functions $u$ and $v$ for the validity of the multidimensional weighted inequality $$\Bigl(\int_E \Phi(T_k f(x))^q u(x)\,dx\Bigr)^{1/q} \le C \Bigl (\int_E \Phi(f(x))^p v(x)\,dx\Bigr )^{1/p},$$ where 0<$p$, $q$<$\infty$, $\Phi$ is a logarithmically convex function, and $T_k$ is an integral operator over star-shaped regions. The condition is also necessary for the exponential integral inequality. Moreover, the estimation of $C$ is given and we apply the obtained results to generalize some multidimensional Levin--Cochran-Lee type inequalities. Keywords:multidimensional inequalities, geometric mean operators, exponential inequalities, star-shaped regionsCategories:26D15, 26D10

22. CMB 2009 (vol 53 pp. 118)

Lewis, Paul
 The Uncomplemented Spaces $W(X,Y)$ and $K(X,Y)$ Classical results of Kalton and techniques of Feder are used to study the complementation of the space $W(X, Y)$ of weakly compact operators and the space $K(X,Y)$ of compact operators in the space $L(X,Y)$ of all bounded linear maps from X to Y. Keywords:spaces of operators, complemented subspace, weakly compact operator, basic sequenceCategories:46B28, 46B15, 46B20

23. CMB 2009 (vol 53 pp. 51)

Cobos, Fernando; Fernández-Cabrera, Luz M.
 On the Relationship Between Interpolation of Banach Algebras and Interpolation of Bilinear Operators We show that if the general real method $(\cdot ,\cdot )_\Gamma$ preserves the Banach-algebra structure, then a bilinear interpolation theorem holds for $(\cdot ,\cdot )_\Gamma$. Keywords:real interpolation, bilinear operators, Banach algebrasCategories:46B70, 46M35, 46H05

24. CMB 2009 (vol 52 pp. 213)

Ghenciu, Ioana; Lewis, Paul
 Dunford--Pettis Properties and Spaces of Operators J. Elton used an application of Ramsey theory to show that if $X$ is an infinite dimensional Banach space, then $c_0$ embeds in $X$, $\ell_1$ embeds in $X$, or there is a subspace of $X$ that fails to have the Dunford--Pettis property. Bessaga and Pelczynski showed that if $c_0$ embeds in $X^*$, then $\ell_\infty$ embeds in $X^*$. Emmanuele and John showed that if $c_0$ embeds in $K(X,Y)$, then $K(X,Y)$ is not complemented in $L(X,Y)$. Classical results from Schauder basis theory are used in a study of Dunford--Pettis sets and strong Dunford--Pettis sets to extend each of the preceding theorems. The space $L_{w^*}(X^* , Y)$ of $w^*-w$ continuous operators is also studied. Keywords:Dunford--Pettis property, Dunford--Pettis set, basic sequence, complemented spaces of operatorsCategories:46B20, 46B28

25. CMB 2008 (vol 51 pp. 618)

Valmorin, V.
 Vanishing Theorems in Colombeau Algebras of Generalized Functions Using a canonical linear embedding of the algebra ${\mathcal G}^{\infty}(\Omega)$ of Colombeau generalized functions in the space of $\overline{\C}$-valued $\C$-linear maps on the space ${\mathcal D}(\Omega)$ of smooth functions with compact support, we give vanishing conditions for functions and linear integral operators of class ${\mathcal G}^\infty$. These results are then applied to the zeros of holomorphic generalized functions in dimension greater than one. Keywords:Colombeau generalized functions, linear integral operators, generalized holomorphic functionsCategories:32A60, 45P05, 46F30
 Page 1 2 Next
 top of page | contact us | privacy | site map |

© Canadian Mathematical Society, 2016 : https://cms.math.ca/