Related papers: Some translation-invariant Banach function spaces …
We present partial results to the following question: Does every infinite dimensional Banach space have an infinite dimensional subspace on which one can define an operator which is not a compact perturbation of a scalar multiplication?
Previous examples of non-type (D) maximal monotone operators were restricted to $\ell^1$, $L^1$, and Banach spaces containing isometriccopies of these spaces. This fact led to the conjecture that non-type (D) operators were restricted to…
In this article we obtain some positive results about the existence of a common nontrivial invariant subspace for $N$-tuples of not necessarily commuting operators on Banach spaces with a Schauder basis. The concept of joint quasinilpotence…
In this paper, we report on new results related to the existence of an adjoint for operators on separable Banach spaces and discuss a few interesting applications. (Some results are new even for Hilbert spaces.) Our first two applications…
We prove, under certain conditions, the existence of zeros for a weakly continuous operator on a paracompact topological space into the dual of a Banach space.
We show that complemented subspaces of uncountable products of Banach spaces are products of complemented subspaces of countable subproducts.
A Banach space X is said to have the Tsirelson property if it does not contain subspaces that are isomorphic to l_{p}, p in [1,infty) or c_{0}. The article contains a quite simple method to producing Banach spaces with the Tsirelson…
We study Hahn-Banach extensions of multilinear forms defined on Banach sequence spaces. We characterize $c_0$ in terms of extension of bilinear forms, and describe the Banach sequence spaces in which every bilinear form admits extensions to…
We prove that the Grand Lebesgue Space, builded on a unimodular locally compact topological group, forms a Banach algebra relative to the convolution.
The question which led to the title of this note is the following: {\it If $X$ is a Banach space and $K$ is a compact subset of $X$, is it possible to find a compact, or even approximable, operator $v:X\to X$ such that…
We prove a number of results linking properties of actions by compact groups (both quantum and classical) on Banach spaces, such as uniform continuity, spectrum finiteness and extensibility of the actions across several constructions.…
On a reflexive Banach space $X$, if an operator $T$ admits a functional calculus for the absolutely continuous functions on its spectrum $\sigma(T) \subseteq \mathbb{R}$, then this functional calculus can always be extended to include all…
In this article, we study spectral Barron spaces whose elements are made up of some vector-valued functions on a compact group whose Fourier transforms admit a certain summability property. We investigate their functional properties and…
The paper is devoted to two particular cases of the following general problem. Let $\alpha$ and $\beta$ be two types of bases in Banach spaces. Let a Banach space $X$ has bases of both types and a subspace $M\subset X^*$ contains the…
We prove an implicit function theorem for functions on infinite-dimensional Banach manifolds, invariant under the (local) action of a finite dimensional Lie group. Motivated by some geometric variational problems, we consider group actions…
We give a self-contained treatment of symmetric Banach sequence spaces and some of their natural properties. We are particularly interested in the symmetry of the norm and the existence of symmetric linear functionals. Many of the presented…
In this paper we survey known results of characterizations of reflexive Banach spaces, which are based on convergence of usual and generalized arithmetic mean (or Ces\`aro sum), weakly compact subsets, affine sets in a Banach space or its…
We prove that finite-spectrum representations of compact quantum groups either in unital $C^*$-algebras $A$ or on Banach spaces $E$ exhibit the same Banach-space-modeled differential-geometric structure as their classical analogues: (a)…
A Banach space E is said to have Property (w) if every (bounded linear) operator from E into E' is weakly compact. We give some interesting examples of James type Banach spaces with Property (w). We also consider the passing of Property (w)…
We introduce and study the notion of overcomplete set in a Banach space, that subsumes and extends the classical concept of overcomplete sequence in a (separable) Banach space. We give existence and non-existence results of overcomplete…