Related papers: Extremal properties of contraction semigroups on $…

For an $(n\ge 2)$-dimensional real Banach space $E$ with unit ball $E_{\le 1}$ and a topological space $X$ arbitrary elements in $C(X,E_{\le 1})$ are always expressible as linear combinations of at most three functions valued in the unit…

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…

A theorem of Siebert asserts that if a sequence of semigroups of probability measures on a Lie group G is weakly convergent to a semigroup of the same type, then the corresponding generating functionals are convergent in the weak operator…

We construct a reflexive Banach space $X_\mathcal{D}$ with an unconditional basis such that all spreading models admitted by normalized block sequences in $X_\mathcal{D}$ are uniformly equivalent to the unit vector basis of $\ell_1$, yet…

On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is…

We study problems of maximal symmetry in Banach spaces. This is done by providing an analysis of the structure of small subgroups of the general linear group GL(X), where X is a separable reflexive Banach space. In particular, we provide…

Let $G$ be a real reductive connected Lie group and $\sigma$ an involution of $G$. Let $H$ denote the identity component of the group of fixed points of $\sigma$, $\mathfrak g$ the Lie algebra of $G$ and $\mathfrak q$ the -1 eigenspace of…

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…

We consider convex monotone $C_0$-semigroups on a Banach lattice, which is assumed to be a Riesz subspace of a $\sigma$-Dedekind complete Banach lattice. Typical examples include the space of all bounded uniformly continuous functions and…

In this paper, we prove the equivalence of reflexive Banach spaces and those Banach spaces which satisfy the following form of Bernstein's Lethargy Theorem. Let $X$ be an arbitrary infinite-dimensional Banach space, and let the real-valued…

We consider the class of Banach space $Y$ for which $c_0$ admits a nontrivial twisted sum with $Y$. We present a characterization of such space $Y$ in terms of properties of the $weak^\ast$ topology on $Y^\ast$. We prove that under the…

A Banach space is $c_0$-saturated if all of its closed infinite dimensional subspaces contain an isomorph of $c_0$. In this article, we study the stability of this property under the formation of direct sums and tensor products. Some of the…

We investigate the differentiability properties of real-valued quasiconvex functions f defined on a separable Banach space X. Continuity is only assumed to hold at the points of a dense subset. If so, this subset is automatically residual.…

We consider a Banach algebra $A$ with the property that, roughly speaking, sufficiently many irreducible representations of $A$ on nontrivial Banach spaces do not vanish on all square zero elements. The class of Banach algebras with this…

A discrete group $\G$ is called rigidly symmetric if the projective tensor product between the convolution algebra $\ell^1(\G)$ and any $C^*$-algebra $\A$ is symmetric. We show that in each topologically graded $C^*$-algebra over a rigidly…

We study some questions concerning the structure of the set of spreading models of a separable infinite-dimensional Banach space $X$. In particular we give an example of a reflexive $X$ so that all spreading models of $X$ contain $\ell_1$…

We study those Banach spaces $X$ for which $S_X$ does not admit a finite $\eps$-net consisting of elements of $S_X$ for any $\eps < 2$. We give characterisations of this class of spaces in terms of $\ell_1$-type sequences and in terms of…

A group G is representable in a Banach space X if G is isomorphic to the group of isometries on X in some equivalent norm. We prove that a countable group G is representable in a separable real Banach space X in several general cases,…

A remarkable theorem of R. C. James is the following: suppose that $X$ is a Banach space and $C \subseteq X$ is a norm bounded, closed and convex set such that every linear functional $x^* \in X^*$ attains its supremum on $C$; then $C$ is a…

Working over infinite dimensional separable Hilbert spaces, residual results have been achieved for the space of contractive $C_{0}$-semigroups under the topology of uniform weak operator convergence on compact subsets of $\mathbb{R}_{+}$.…