Related papers: Single and multi-valued Hilbert-bundle renormings

Given a Banach space we consider the $\sigma$-ideal of all of its subsets which are covered by countably many hyperplanes and investigate its standard cardinal characteristics as the additivity, the covering number, the uniformity, the…

We show three Hahn-Banach type extension criteria for (sets of) bounded C*-linear maps of Hilbert C*-modules to the underlying C*-algebras of coefficients. One criterion establishes an alternative description of the property of (AW*-)…

We consider a compact complex manifold $M$, and introduce the notion of two holomorphic Banach bundles $E,F$ over $M$ being compact perturbations of one another. Given two such bundles we show that if the cohomology groups $H^q(M,E)$ are…

We show, e.g., that a holomorphic Banach vector bundle over a pseudoconvex open subset of, say, Hilbert space is holomorphically trivial if it is continuously trivial. Some applications are also given.

We consider homomorphisms of hermitian holomorphic Hilbert bundles. Assuming the homomorphism decreases curvature, we prove that its pointwise norm is plurisubharmonic.

Given a category of objects, it is both useful and important to know if all the objects in the category may be realised as sub-objects -- via morphisms in the given category -- of a single object in that category enjoying some nice…

We prove several results asserting that the action of a Banach-Lie group on Hilbert spaces of holomorphic sections of a holomorphic Hilbert space bundle over a complex Banach manifold is multiplicity free. These results require the…

We give a notion of equivalence for Fell bundles over groups, not necessarily saturated nor separable, and show that equivalent Fell bundles have Morita-Rieffel equivalent cross-sectional $C^*$-algebras. Our notion is originated in the…

We present and study a family of metrics on the space of compact subsets of $R^N$ (that we call ``shapes''). These metrics are ``geometric'', that is, they are independent of rotation and translation; and these metrics enjoy many…

We show that for a $\sigma $-ideal $\ci$ with a Steinhaus property defined on Banach space, if two non-homeomorphic Banach with the same cardinality of the Hamel basis then there is a $\ci$ nonmeasurable subset as image by any isomorphism…

In this paper, we characterize homogeneous arithmetically Cohen-Macaulay (ACM) bundles and Ulrich bundles on rational homogeneous spaces. %with respect to general polarizations. From this result, we see that there are only finitely many…

It is consistent with any possible value of the continuum $\mathfrak{c}$ that every infinite-dimensional Banach space of density $\leq \mathfrak{c}$ condenses onto the Hilbert cube. Let $\mu$ be a cardinal of uncountable cofinality. It is…

In this short note, we give some new results on continuous bounded cohomology groups of topological semigroups with values in complex field. We show that the second continuous bounded cohomology group of a compact metrizable semigroup, is a…

Purpose: A new point of view in the study of impact is introduced. Approach: Using fundamental theorems in real analysis we study the convergence of well-known impact measures. Findings: We show that pointwise convergence is maintained by…

We present a general approach to a modular frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…

We show that the category of affine bundles over a smooth manifold M is equivalent to the category of affine spaces modelled on projective finitely generated C^\infty(M)-modules. Using this equivalence of categories, we are able to give an…

Representations of $C^*$-algebras are realized on section spaces of holomorphic homogeneous vector bundles. The corresponding section spaces are investigated by means of a new notion of reproducing kernel, suitable for dealing with…

We extend an old result of de la Harpe and Karoubi, concerning almost representations of compact groups, to proper groupoids admitting continuous Haar measure systems. As an application, we establish the existence of sufficiently many…

For a locally compact group $G$ and a compact subgroup $H$, we show that the Banach space $M(G/H)$ may be considered as a quotient space of $M(G)$. Also, we define a convolution on $M(G/H)$ which makes it into a Banach algebra. It may be…