Expand all Collapse all | Results 1 - 15 of 15 |
1. CMB Online first
Characters on $C( X)$ The precise condition on a completely regular space $X$ for every character on
$C(X) $ to be an evaluation at some point in $X$ is that $X$ be
realcompact. Usually, this classical result is obtained relying heavily on
involved (and even nonconstructive) extension arguments. This note provides a
direct proof that is accessible to a large audience.
Keywords:characters, realcompact, evaluation, real-valued continuous functions Categories:54C30, 46E25 |
2. CMB Online first
Real Hypersurfaces in Complex Two-Plane Grassmannians with Reeb Parallel Structure Jacobi Operator In this paper we give a characterization of a real hypersurface of
Type~$(A)$ in complex two-plane Grassmannians ${ { {G_2({\mathbb
C}^{m+2})} } }$, which means a
tube over a totally geodesic $G_{2}(\mathbb C^{m+1})$ in
${G_2({\mathbb C}^{m+2})}$, by
the Reeb parallel structure Jacobi operator ${\nabla}_{\xi}R_{\xi}=0$.
Keywords:real hypersurfaces, complex two-plane Grassmannians, Hopf hypersurface, Reeb parallel, structure Jacobi operator Categories:53C40, 53C15 |
3. CMB 2012 (vol 56 pp. 640)
Regulator Indecomposable Cycles on a Product of Elliptic Curves We provide a novel proof of the existence
of regulator indecomposables in the cycle group $CH^2(X,1)$,
where $X$ is a sufficiently general product of two elliptic
curves. In particular, the nature of our proof provides an illustration of
Beilinson rigidity.
Keywords:real regulator, regulator indecomposable, higher Chow group, indecomposable cycle Category:14C25 |
4. CMB 2011 (vol 56 pp. 306)
Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator is Lie $\mathbb{D}$-parallel |
Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator is Lie $\mathbb{D}$-parallel We prove the non-existence of real hypersurfaces in complex projective
space whose structure Jacobi operator is Lie $\mathbb{D}$-parallel and
satisfies a further condition.
Keywords:complex projective space, real hypersurface, structure Jacobi operator Categories:53C15, 53C40 |
5. CMB 2011 (vol 55 pp. 752)
Approximation of Holomorphic Solutions of a System of Real Analytic Equations We prove the existence of an approximation function for holomorphic
solutions of a system of real analytic equations. For this we use
ultraproducts and Weierstrass systems introduced by J. Denef and L.
Lipshitz. We also prove a version of the PÅoski smoothing theorem in
this case.
Keywords:Artin approximation, real analytic equations Categories:13B40, 13L05, 14F12 |
6. CMB 2011 (vol 55 pp. 611)
Chen Inequalities for Submanifolds of Real Space Forms with a Semi-Symmetric Non-Metric Connection In this paper we prove Chen inequalities for submanifolds of real space
forms endowed with a semi-symmetric non-metric connection, i.e., relations
between the mean curvature associated with a semi-symmetric non-metric
connection, scalar and sectional curvatures, Ricci curvatures and the
sectional curvature of the ambient space. The equality cases are considered.
Keywords:real space form, semi-symmetric non-metric connection, Ricci curvature Categories:53C40, 53B05, 53B15 |
7. CMB 2011 (vol 55 pp. 114)
On Characterizations of Real Hypersurfaces in a Complex Space Form with $\eta$-Parallel Shape Operator |
On Characterizations of Real Hypersurfaces in a Complex Space Form with $\eta$-Parallel Shape Operator In this paper we study real hypersurfaces in a non-flat complex space form with $\eta$-parallel shape operator. Several partial characterizations of these real hypersurfaces are obtained.
Keywords:complex space form, Hopf hypersurfaces, ruled real hypersurfaces, $\eta$-parallel shape operator Categories:53C40, 53C15 |
8. CMB 2011 (vol 54 pp. 422)
Two Conditions on the Structure Jacobi Operator for Real Hypersurfaces in Complex Projective Space We classify real hypersurfaces in complex projective space whose
structure Jacobi operator satisfies two conditions at the same time.
Keywords:complex projective space, real hypersurface, structure Jacobi operator, two conditions Categories:53C15, 53B25 |
9. CMB 2011 (vol 54 pp. 593)
Stability of Real $C^*$-Algebras We will give a characterization of stable real $C^*$-algebras
analogous to the one given for complex $C^*$-algebras by Hjelmborg
and RÃ¸rdam. Using this result, we will prove
that any real $C^*$-algebra satisfying the corona factorization
property is stable if and only if its complexification is stable.
Real $C^*$-algebras satisfying the corona factorization property
include AF-algebras and purely infinite $C^*$-algebras. We will also
provide an example of a simple unstable $C^*$-algebra, the
complexification of which is stable.
Keywords:stability, real C*-algebras Category:46L05 |
10. CMB 2009 (vol 53 pp. 51)
On the Relationship Between Interpolation of Banach Algebras and Interpolation of Bilinear Operators |
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 algebras Categories:46B70, 46M35, 46H05 |
11. CMB 2009 (vol 52 pp. 39)
A Representation Theorem for Archimedean Quadratic Modules on $*$-Rings We present a new approach to noncommutative real algebraic geometry
based on the representation theory of $C^\ast$-algebras.
An important result in commutative real algebraic geometry is
Jacobi's representation theorem for archimedean quadratic modules
on commutative rings.
We show that this theorem is a consequence of the
Gelfand--Naimark representation theorem for commutative $C^\ast$-algebras.
A noncommutative version of Gelfand--Naimark theory was studied by
I. Fujimoto. We use his results to generalize
Jacobi's theorem to associative rings with involution.
Keywords:Ordered rings with involution, $C^\ast$-algebras and their representations, noncommutative convexity theory, real algebraic geometry Categories:16W80, 46L05, 46L89, 14P99 |
12. CMB 2008 (vol 51 pp. 359)
Real Hypersurfaces in Complex Space Forms with Reeb Flow Symmetric Structure Jacobi Operator Real hypersurfaces in a complex space form whose structure
Jacobi operator is symmetric along the Reeb flow are studied. Among
them, homogeneous real hypersurfaces of type $(A)$ in a complex
projective or hyperbolic space are characterized as those whose structure
Jacobi operator commutes with the shape operator.
Keywords:complex space form, real hypersurface, structure Jacobi operator Categories:53B20, 53C15, 53C25 |
13. CMB 2005 (vol 48 pp. 561)
A Note on Lagrangian Loci of Quotients We study Hamiltonian actions of compact groups in the presence of
compatible involutions. We show that the Lagrangian fixed point set
on the symplectically reduced space is isomorphic to the disjoint
union of the involutively reduced spaces corresponding to
involutions on the group strongly inner to the given one.
Our techniques imply that the solution to the eigenvalues of a sum problem
for a given real form can be reduced to the quasi-split real form in the
same inner class. We also consider invariant quotients with respect to
the corresponding real form of the complexified group.
Keywords:Quotients, involutions, real forms, Lagrangian loci Category:53D20 |
14. CMB 2005 (vol 48 pp. 121)
Necessary and Sufficient Conditions for the Central Norm to Equal $2^h$ in the Simple Continued Fraction Expansion of $\sqrt{2^hc}$ for Any Odd $c>1$ |
Necessary and Sufficient Conditions for the Central Norm to Equal $2^h$ in the Simple Continued Fraction Expansion of $\sqrt{2^hc}$ for Any Odd $c>1$ We look at the simple continued fraction expansion of $\sqrt{D}$
for any $D=2^hc $ where $c>1$ is odd with a goal of
determining necessary and
sufficient conditions for the central norm (as determined by
the infrastructure of the underlying real quadratic order therein) to be
$2^h$. At the end of the paper, we also address the case where $D=c$
is odd and the central norm of $\sqrt{D}$ is equal to $2$.
Keywords:quadratic Diophantine equations, simple continued fractions,, norms of ideals, infrastructure of real quadratic fields Categories:11A55, 11D09, 11R11 |
15. CMB 1999 (vol 42 pp. 274)
The Bockstein Map is Necessary We construct two non-isomorphic nuclear, stably finite,
real rank zero $C^\ast$-algebras $E$ and $E'$ for which
there is an isomorphism of ordered groups
$\Theta\colon \bigoplus_{n \ge 0} K_\bullet(E;\ZZ/n) \to
\bigoplus_{n \ge 0} K_\bullet(E';\ZZ/n)$ which is compatible
with all the coefficient transformations. The $C^\ast$-algebras
$E$ and $E'$ are not isomorphic since there is no $\Theta$
as above which is also compatible with the Bockstein operations.
By tensoring with Cuntz's algebra $\OO_\infty$ one obtains a pair
of non-isomorphic, real rank zero, purely infinite $C^\ast$-algebras
with similar properties.
Keywords:$K$-theory, torsion coefficients, natural transformations, Bockstein maps, $C^\ast$-algebras, real rank zero, purely infinite, classification Categories:46L35, 46L80, 19K14 |