Related papers: A Representation of Stable Banach Spaces

We show that if $T$ is an isometry (as metric spaces) between the invertible groups of unital Banach algebras, then $T$ is extended to a surjective real-linear isometry up to translation between the two Banach algebras. Furthermore if the…

We prove that any convex-like structure in the sense of Nate Brown is affinely and isometrically isomorphic to a closed convex subset of a Banach space. This answers an open question of Brown. As an intermediate step, we identify Brown's…

We study Banach spaces whose group of isometries acts micro-transitively on the unit sphere. We introduce a weaker property, which one-complemented subspaces inherit, that we call uniform micro-semitransitivity. We prove a number of results…

The paper emphasizes the property of stability for skew-evolution semiflows on Banach spaces, defined by means of evolution semiflows and evolution cocycles and which generalize the concept introduced by us in a previous paper. There are…

In this paper we explore the method of holomorphic induction for unitary representations of Banach--Lie groups. First we show that the classification of complex bundle structures on homogeneous Banach bundles over complex homogeneous spaces…

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

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 analogy to a recent result by V. Fonf, M. Lin, and P. Wojtaszczyk, we prove the following characterizations of a Banach space $X$ with a basis. (i) $X$ is finite-dimensional if and only if every bounded, uniformly continuous, mean…

In this paper we generalize a result in [1], showing that an arbitrary Riemannian symmetric space can be realized as a closed submanifold of a covering group of the Lie group defining the symmetric space. Some properties of the subgroups of…

We prove the absolute continuity of stable foliations for mappings of Banach spaces satisfying conditions consistent with time-t maps of certain classes of dissipative PDEs. This property is crucial for passing information from submanifolds…

To each 2-dimensional irreducible p-adic representation of Gal(Qpbar/Qp) which becomes crystalline over an abelian extension of Q_p, we associate a Banach space B(V) endowed with a linear continuous unitary action of GL_2(Q_p). When V is…

We study the complexities of isometry and isomorphism classes of separable Banach spaces in the Polish spaces of Banach spaces recently introduced and investigated by the authors in [14]. We obtain sharp results concerning the most…

We show that lattice isomorphisms between lattices of slowly oscillating functions on chain-connected proper metric spaces induce coarsely equivalent homeomorphisms. This result leads to a Banach-Stone-like theorem for these lattices.…

In this paper we present new characterizations of Banach spaces whose duals are isomorphic to $l_{1}(\Gamma),$ extending results of Stegall, Lewis-Stegall and Cilia-D'Anna-Guti\'{e}rrez.

A Banach space $X$ is elastic if there is a constant $K$ so that whenever a Banach space $Y$ embeds into $X$, then there is an embedding of $Y$ into $X$ with constant $K$. We prove that $C[0,1]$ embeds into separable infinite dimensional…

In \cite[\S1.3]{Br2}, some unitary representations of ${\rm GL}_2(\mathbf{Q}_p)$ on $p$-adic Banach spaces are associated to 2-dimensional irreducible crystalline representations of ${\rm Gal}(\bar{\mathbf{Q}}_p)/\mathbf{Q}_p)$. Some…

We give new and simple proofs of some classical properties of hereditarily indecomposable Banach spaces, including the result by W. T. Gowers and B. Maurey that a hereditarily indecomposable Banach space cannot be isomorphic to a proper…

A Banach space is said to have the Lebesgue property if every Riemann-integrable function $f:[0,1]\to X$ is Lebesgue almost everywhere continuous. We give a characterization of the Lebesgue property in terms of a new sequential asymptotic…

We show that if $T$ is an isometry (as metric spaces) from an open subgroup of the group of the invertible elements in a unital semisimple commutative Banach algebra onto an open subgroup of the group of the invertible elements in a unital…

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.…