Related papers: Banach Spaces Which Embed into their Dual

The main result says that every surjective isometry between two ideal Banach function spaces satisfying certain conditions can be presented as a composition of a measurable transformation of a variable and multiplication by a function.

We show that a representation of a Banach algebra $A$ on a Banach space $X$ can be extended to a canonical representation of $A^{**}$ on $X$ if and only if certain orbit maps $A\to X$ are weakly compact. When this is the case, we show that…

We study random unconditional convergence for a basis in a Banach space. The connections between this notion and classical unconditionality are explored. In particular, we analyze duality relations, reflexivity, uniqueness of these bases…

We study properties of representing and absolutely representing systems of subspaces in Banach spaces. We also present sufficient conditions for the system of subspaces to be a representing system of subspaces.

We prove the Zabreiko's lemma in 2-Banach spaces. As an application we shall prove a version of the closed graph theorem and open mapping theorem.

We prove the version of interpolation theorem for non-commutative vector-valued fully symmetric spaces associated with fully symmetric Banach function spaces and a von Neumann algebra equipped with a faithful semifinite normal trace.

The problems connected with equivalent norms lie at the heart of Banach space theory. This is a short survey on some recent as well as classical results and open problems in renormings of Banach spaces.

This paper studies Schauder frames in Banach spaces, a concept which is a natural generalization of frames in Hilbert spaces and Schauder bases in Banach spaces. The associated minimal and maximal spaces are introduced, as are shrinking and…

We introduce algebras which are inductive limits of Banach spaces and carry inequalities which are counterparts of the inequality for the norm in a Banach algebra. We then define an associated Wiener algebra, and prove the corresponding…

An algebra of bounded linear operators on a Banach space is said to be {\em strongly compact} if its unit ball is precompact in the strong operator topology, and a bounded linear operator on a Banach space is said to be {\em strongly…

In this paper we study ways to establish when a Banach space can be identified as the dual or the double dual of another Banach space. To obtain these results, we relate these spaces with other, concrete Banach spaces - tipically $\ell^1$…

We introduce a novel real-valued endogenous logic for expressing properties of probabilistic transition systems called Riesz modal logic. The design of the syntax and semantics of this logic is directly inspired by the theory of Riesz…

Necessary and sufficient conditions for Banach space to be(isometrically isomorphic to) a dual space will be given.

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 combine functional analytic and geometric viewpoints on approximate Birkhoff and isosceles orthogonality in generalized Minkowski spaces which are finite-dimensional vector spaces equipped with a gauge. This is the first approach to…

In this paper, we define probabilistic n-Banach spaces along with some concepts in this field and study convergence in these spaces by some lemmas and theorem.

We prove the existence of the invariant subspaces of some operators in a real Banach space. For example, linear isometries have invariant subspaces

We show that if the Szlenk index of a Banach space $X$ is larger than the first infinite ordinal $\omega$ or if the Szlenk index of its dual is larger than $\omega$, then the tree of all finite sequences of integers equipped with the…

In this article we introduce and investigate some new Banach spaces, so - called moment spaces, and consider applications to the Fourier series, singular integral operators, theory of martingales.

We discuss some open problems in the Geometry of Banach spaces having Ramsey-theoretic flavor. The problems are exposed together with well known results related to them.