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Search: MSC category 47B38 ( Operators on function spaces (general) )

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1. 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

2. CMB 2013 (vol 57 pp. 794)

Fang, Zhong-Shan; Zhou, Ze-Hua
 New Characterizations of the Weighted Composition Operators Between Bloch Type Spaces in the Polydisk We give some new characterizations for compactness of weighted composition operators $uC_\varphi$ acting on Bloch-type spaces in terms of the power of the components of $\varphi,$ where $\varphi$ is a holomorphic self-map of the polydisk $\mathbb{D}^n,$ thus generalizing the results obtained by HyvÃ¤rinen and LindstrÃ¶m in 2012. Keywords:weighted composition operator, compactness, Bloch type spaces, polydisk, several complex variablesCategories:47B38, 47B33, 32A37, 45P05, 47G10

3. CMB 2011 (vol 56 pp. 593)

Liu, Congwen; Zhou, Lifang
 On the $p$-norm of an Integral Operator in the Half Plane We give a partial answer to a conjecture of DostaniÄ on the determination of the norm of a class of integral operators induced by the weighted Bergman projection in the upper half plane. Keywords:Bergman projection, integral operator, $L^p$-norm, the upper half planeCategories:47B38, 47G10, 32A36

4. 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

5. CMB 2010 (vol 53 pp. 466)

Dubarbie, Luis
 Separating Maps between Spaces of Vector-Valued Absolutely Continuous Functions In this paper we give a description of separating or disjointness preserving linear bijections on spaces of vector-valued absolutely continuous functions defined on compact subsets of the real line. We obtain that they are continuous and biseparating in the finite-dimensional case. The infinite-dimensional case is also studied. Keywords:separating maps, disjointness preserving, vector-valued absolutely continuous functions, automatic continuityCategories:47B38, 46E15, 46E40, 46H40, 47B33

6. CMB 2008 (vol 51 pp. 481)

Bayart, Frédéric
 Universal Inner Functions on the Ball It is shown that given any sequence of automorphisms $(\phi_k)_k$ of the unit ball $\bn$ of $\cn$ such that $\|\phi_k(0)\|$ tends to $1$, there exists an inner function $I$ such that the family of non-Euclidean translates" $(I\circ\phi_k)_k$ is locally uniformly dense in the unit ball of $H^\infty(\bn)$. Keywords:inner functions, automorphisms of the ball, universalityCategories:32A35, 30D50, 47B38

7. CMB 2007 (vol 50 pp. 172)

Aron, Richard; Gorkin, Pamela
 An Infinite Dimensional Vector Space of Universal Functions for $H^\infty$ of the Ball We show that there exists a closed infinite dimensional subspace of $H^\infty(B^n)$ such that every function of norm one is universal for some sequence of automorphisms of $B^n$. Categories:47B38, 47B33, 46J10

8. CMB 2005 (vol 48 pp. 409)

Gauthier, P. M.; Xiao, J.
 The Existence of Universal Inner Functions on the Unit Ball of $\mathbb{C}^n$ It is shown that there exists an inner function $I$ defined on the unit ball ${\bf B}^n$ of ${\mathbb C}^n$ such that each function holomorphic on ${\bf B}^n$ and bounded by $1$ can be approximated by `non-Euclidean translates" of $I$. Keywords:universal inner functionsCategories:32A35, 30D50, 47B38

9. CMB 2004 (vol 47 pp. 456)

Seto, Michio
 On the Berger-Coburn-Lebow Problem for Hardy Submodules In this paper we shall give an affirmative solution to a problem, posed by Berger, Coburn and Lebow, for $C^{\ast}$-algebras on Hardy submodules. Keywords:Hardy submodulesCategory:47B38

10. CMB 2004 (vol 47 pp. 49)

Lindström, Mikael; Makhmutov, Shamil; Taskinen, Jari
 The Essential Norm of a Bloch-to-$Q_p$ Composition Operator The $Q_p$ spaces coincide with the Bloch space for $p>1$ and are subspaces of $\BMOA$ for $0 Keywords:Bloch space, little Bloch space,$\BMOA$,$\VMOA$,$Q_p$spaces,, composition operator, compact operator, essential normCategories:47B38, 47B10, 46E40, 46E15 11. CMB 1999 (vol 42 pp. 139) Bonet, José; Domański, Paweł; Lindström, Mikael  Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions Every weakly compact composition operator between weighted Banach spaces$H_v^{\infty}$of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space$H_v^{\infty}$are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces. Keywords:weighted Banach spaces of holomorphic functions, composition operator, compact operator, weakly compact operatorCategories:47B38, 30D55, 46E15 12. CMB 1998 (vol 41 pp. 129) Lee, Young Joo  Pluriharmonic symbols of commuting Toeplitz type operators on the weighted Bergman spaces A class of Toeplitz type operators acting on the weighted Bergman spaces of the unit ball in the$n$-dimensional complex space is considered and two pluriharmonic symbols of commuting Toeplitz type operators are completely characterized. Keywords:Pluriharmonic functions, Weighted Bergman spaces, Toeplitz type operators.Categories:47B38, 32A37 13. CMB 1997 (vol 40 pp. 193) Kucerovsky, Dan  Finite rank operators and functional calculus on Hilbert modules over abelian$C^{\ast}$-algebras We consider the problem: If$K$is a compact normal operator on a Hilbert module$E$, and$f\in C_0(\Sp K)$is a function which is zero in a neighbourhood of the origin, is$f(K)$of finite rank? We show that this is the case if the underlying$C^{\ast}$-algebra is abelian, and that the range of$f(K)$is contained in a finitely generated projective submodule of$E\$. Categories:55R50, 47A60, 47B38
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