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

Concentration compactness method is a powerful techniques for establishing existence of minimizers for inequalities and of critical points of functionals in general. The paper gives a functional-analytic formulation for the method in Banach…

We study the Hausdorff distance between a set and its convex hull. Let $X$ be a Banach space, define the CHD-module of space $X$ as the supremum of this distance for all subset of the unit ball in $X$. In the case of finite dimensional…

When identified with sequences of irreducible Hermitian-Einstein connections, sequences of stable holomorphic bundles of fixed topological type and bounded degree on a compact complex surface equipped with a Gauduchon metric are shown to…

In the present paper we study bundles equipped with extra homotopy conditions, in particular so-called simplicial $n$-bundles. It is shown that (under some condition) the classifying space of 1-bundles is the double coset space of some…

Let C be an axiomatizable class of order continuous real or complex Banach lattices, that is, this class is closed under isometric vector lattice isomorphisms and ultraproducts, and the complementary class is closed under ultrapowers. We…

Defect of compactness for non-compact imbeddings of Banach spaces can be expressed in the form of a profile decomposition. This paper extends the profile decomposition for Sobolev spaces proved by Solimini (AIHP 1995) to the non-reflexive…

We introduce a new topological property called (*) and the corresponding class of topological spaces, which includes spaces with $G_\delta$-diagonals and Gruenhage spaces. Using (*), we characterise those Banach spaces which admit…

In a previous paper the second author introduced a compact topology on the space of closed ideals of a unital Banach algebra A. If A is separable then this topology is either metrizable or else neither Hausdorff nor first countable. Here it…

We construct a Banach space satisfying that the nearest point map (also called proximity mapping or metric projection) onto any compact and convex subset is continuous but not uniformly continuous. The space we construct is locally…

We construct new complete, compact, inhomogeneous Einstein metrics on S^{m+2} sphere bundles over 2n-dimensional Einstein-Kahler spaces K_{2n}, for all n \ge 1 and all m \ge 1. We also obtain complete, compact, inhomogeneous Einstein…

We construct examples of flat fiber bundles over the Hopf surface such that the total spaces have no pseudoconvex neighborhood basis, admit a complete K\"ahler metric, or are hyperconvex but have no nonconstant holomorphic functions. For…

It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$. Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear…

In this paper we investigate some reflexivity-type properties of separable measurable Banach bundles over a $\sigma$-finite measure space. Our two main results are the following: - The fibers of a bundle are uniformly convex (with a common…

We show that every infinite crowded space can be mapped onto a homogeneous space of countable weight, and that there is a homogeneous space of weight continuum that cannot be mapped onto a homogeneous space of uncountable weight strictly…

Let B be a unital Banach algebra. A projection in B which is equivalent to the identitity may give rise to a matrix-like structure on any two-sided ideal A in B. In this set-up we prove a theorem to the effect that the bounded Hochschild…

Two new classes of metrizable vector bundles have been presented in the papers [1] and [4]. The Lie algebroid generalized tangent bundle of a dual vector bundle is presented. This Lie algebroid is a new example of metrizable vector bundle.…

We investigate quantization properties of Hermitian metrics on holomorphic vector bundles over homogeneous compact K\"ahler manifolds. This allows us to study operators on Hilbert function spaces using vector bundles in a new way. We show…

If $H$ is a lattice in a locally compact second countable group $G$, then we show that $G$ has property A (respectively is coarsely embeddable into Hilbert space) if and only if $H$ has property A (respectively is coarsely embeddable into…

Cocompactness is a property of embeddings between two Banach spaces, similar to but weaker than compactness, defined relative to some non-compact group of bijective isometries. In presence of a cocompact embedding, bounded sequences (in the…

A problem of Banach asks whether every infinite-dimensional Banach space which is isomorphic to all its infinite-dimensional subspaces must be isomorphic to a separable Hilbert space. In this paper we prove a result of a Ramsey-theoretic…