Related papers: A new proof of James' sup theorem

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…

A subset of a Banach space is called equilateral if the distances between any two of its distinct elements are the same. It is proved that there exist non-separable Banach spaces (in fact of density continuum) with no infinite equilateral…

In this paper, using generalized metric projection, we propose a new extragradient method for finding a common element of the solutions set of a generalized equilibrium problem and a variational inequality for an $\alpha$-inverse-strongly…

This paper is concerned with the isomorphic structure of the Banach space $\ell_\infty/c_0$ and how it depends on combinatorial tools whose existence is consistent but not provable from the usual axioms of ZFC. Our main global result is…

It is well known in Banach space theory that for a finite dimensional space $E$ there exists a constant $c_E$, such that for all sequences $(x_k)_k \subset E$ one has \[ \summ_k \noo x_k \rrm \kl c_E \pl \sup_{\eps_k \pm 1} \noo \summ_k…

We prove that no separable Banach algebra is universal for homomorphic embeddings of all separable Banach algebras, whether embeddings are merely bounded or required to be contractive. The same holds in the commutative category. The proof…

In this work, conditions are provided under which a normed double sum of independent random elements in a real separable Rademacher type $p$ Banach space converges completely to $0$ in mean of order $p$. These conditions for the complete…

We prove existence of wide types in a continuous theory expanding a Banach space, and density of minimal wide types among stable types in such a theory. We show that every minimal wide stable type is "generically" isometric to an l_2 space.…

This paper contains results concerning the Borel reduction of the relation $E_0$ of eventual agreement between sequences of 0's and 1's, to the relation of permutative equivalence between basic sequences in a Banach space. For more clarity…

Let $(M,d)$ be a bounded countable metric space and $c>0$ a constant, such that $d(x,y)+d(y,z)-d(x,z) \ge c$, for any pairwise distinct points $x,y,z$ of $M$. For such metric spaces we prove that they can be isometrically embedded into any…

In this paper we prove a strong Hahn-Banach theorem: separation of disjoint convex sets by linear forms is possible without any further conditions, if the target field $\R$ is replaced by a more general real closed extension field. From…

Let $E$ be a Banach space with the $c^1$-norm $\|\cdot\|$ in $ E \backslash \{0\}$ and $S(E)=\{e\in E: \|e\|=1\}.$ In this paper, a geometry characteristic for $E$ is presented by using a geometrical construct of $S(E).$ That is, the…

We prove that Hilbert space is distortable and, in fact, arbitrarily distortable. This means that for all lambda >1 there exists an equivalent norm |.| on l_2 such that for all infinite dimensional subspaces Y of l_2 there exist x,y in Y…

The Banach isometric conjecture asserts that a normed space with all of its $k$-dimensional subspaces isometric, where $k\geq 2$, is Euclidean. The first case of $k=2$ is classical, established by Auerbach, Mazur and Ulam using an elegant…

Let $A$ be a semisimple Banach algebra with non-trivial, and possibly infinite-dimensional socle. Addressing a problem raised by Harte and Hernandez, we first define a characteristic polynomial for elements belonging to the socle, and we…

Let $E$ be one of the spaces $C(K)$ and $L_1$, $F$ be an arbitrary Banach space, $p>1,$ and $(X,\sigma)$ be a space with a finite measure. We prove that $E$ is isometric to a subspace of the Lebesgue-Bochner space $L_p(X;F)$ only if $E$ is…

Let $\mathscr{A}$ be a nonempty set of infinite matrices of linear operators between two topological vector spaces. We show that a sequence is uniformly $\mathscr{A}$-summable if and only if it is $B$-summable for all matrices $B$ of linear…

We study finite subsets of $\ell_p$ and show that, up to nowhere dense and Haar null complement, all of them embed isometrically into any Banach space that uniformly contains the spaces $\ell_p^n$, $n \in \mathbb{N}$.

We study linear and algebraic structures in sets of Dirichlet series with maximal Bohr's strip. More precisely, we consider a set $\mathscr M$ of Dirichlet series which are uniformly continuous on the right half plane and whose strip of…

The class of uniformly smooth hyperbolic spaces was recently introduced by the first author as a common generalization of both CAT(0) spaces and uniformly smooth Banach spaces, in a way that Reich's theorem on resolvent convergence could…