Related papers: Banach spaces from a construction scheme
A subsequence principle is obtained, characterizing Banach spaces containing $c_0$, in the spirit of the author's 1974 characterization of Banach spaces containing $\ell^1$. Definition: A sequence $(b_j)$ in a Banach space is called {\it…
We give a criterion ensuring that the elementary class of a modular Banach space E (that is, the class of Banach spaces, some ultrapower of which is linearly isometric to an ultrapower of E) consists of all direct sums E\oplus_m H, where H…
We study the existence of uncountable first-order structures that are homogeneous with respect to their finitely generated substructures. In many classical cases this is either well-known or follows from general facts, for example, if the…
We show that complemented subspaces of uncountable products of Banach spaces are products of complemented subspaces of countable subproducts.
In this short note, we first consider some inequalities for comparison of some algebraic properties of two continuous algebra-multiplications on an arbitrary Banach space and then, as an application, we consider some very basic observations…
We construct a Banach Poisson-Lie group structure on the unitary group of a separable complex Hilbert space.
We show in this paper that every bijective linear isometry between the continuous section spaces of two non-square Banach bundles gives rise to a Banach bundle isomorphism. This is to support our expectation that the geometric structure of…
An infinite dimensional notion of asymptotic structure is considered. This notion is developed in terms of trees and branches on Banach spaces. Every countably infinite countably branching tree $\mathcal T$ of a certain type on a space X is…
We prove a number of decoupling inequalities for nonhomogeneous random polynomials with coefficients in Banach space. Degrees of homogeneous components enter into comparison as exponents of multipliers of terms of certain Poincar\'e-type…
We survey recent developments on the structure of complemented subspaces of Banach lattices, including in particular the construction of a complemented subspace of a $C(K)$-space which is not linearly isomorphic to any Banach lattice.…
A reflexive Banach space with an unconditional basis admits an equivalent $1$-unconditional $2R$ norm and embeds into a reflexive space with a $1$-symmetric $2R$ norm. Partial results on $1$-symmetric $2R$ renormings of spaces with a…
A hereditarily indecomposable Banach space $\mathfrak{X}_{\mathfrak{nr}}$ is constructed that is the first known example of a $\mathscr{L}_\infty$-space not containing $c_0$, $\ell_1$, or reflexive subspaces and answers a question posed by…
We present a Banach space $\mathfrak X$ with a Schauder basis of length $\omega\_1$ which is saturated by copies of $c\_0$ and such that for every closed decomposition of a closed subspace $X=X\_0\oplus X\_1$, either $X\_0$ or $X\_1$ has to…
In this paper, we introduce the concept of biamenability of Banach algebras and we show that despite the apparent similarities between amenability and biamenability of Banach algebras, they lead to very different, and somewhat opposed,…
An L-embedded Banach spaace is a Banach space which is complemented in its bidual such that the norm is additive between the two complementary parts. On such spaces we define a topology, called an abstract measure topology, which by known…
We study the problem of the existence of unconditional basic sequences in Banach spaces of high density. We show, in particular, the relative consistency with GCH of the statement that every Banach space of density $\aleph_\omega$ contains…
We provide a criterion for $\varepsilon$-hypercyclicity. Also, we extend the ideas of Badea, Grivaux, M\"uller and Bayart to construct $\varepsilon$-hypercyclic operators which are not hypercyclic in a wider class of separable Banach…
Let $X$ and $Y$ be Banach spaces such that the ideal of operators which factor through $Y$ has codimension one in the Banach algebra $\mathscr{B}(X)$ of all bounded operators on $X$, and suppose that $Y$ contains a complemented subspace…
We introduce a class of analytic sheaves in a Banach space X, that we call cohesive sheaves. Cohesion is meant to generalize the notion of coherence from finite dimensional analysis. Accordingly, we prove the analog of Cartan's Theorems A…
In this survey, we present several results related to characterizing the surjective isometries on Banach sequence spaces. Our survey includes full proofs of these characterizations for the classical spaces as well as more recent results for…