A Banach space is polyhedral if the unit ball of each of its finite dimensional subspaces is a polyhedron. It is known that a polyhedral Banach space has a separable dual and is c0-saturated, i.e., each closed infinite dimensional subspace contains an isomorph of c0. In this paper, we show that the Orlicz sequence space hM is isomorphic to a polyhedral Banach space if limt→0 M(Kt)/M(t) = ∞ for ...

we consider the transitive linear maps on the operator algebra $b(x)$for a separable banach space $x$. we show if a bounded linear map is norm transitive on $b(x)$,then it must be hypercyclic with strong operator topology. also we provide a sot-transitivelinear map without being hypercyclic in the strong operator topology.

begin{abstract} in this paper, we prove some strong and weak convergence of three step random iterative scheme with errors to common random fixed points of three asymptotically nonexpansive nonself random mappings in a real uniformly convex separable banach space. end{abstract}

For every α < ω1 we establish the existence of a separable Banach space whose Szlenk index is ω and which is universal for all separable Banach spaces whose Szlenkindex does not exceed ω. In order to prove that result we provide an intrinsic characterization of which Banach spaces embed into a space admitting an FDD with upper estimates.

We prove that the dual or any quotient of a separable reflexive Banach space with the unconditional tree property has the unconditional tree property. This is used to prove that a separable reflexive Banach space with the unconditional tree property embeds into a reflexive Banach space with an unconditional basis. This solves several long standing open problems. In particular, it yields that a ...

We show that when a linear quotient map to a separable Banach space X has a Lipschitz right inverse, then it has a linear right inverse. If a separable space X embeds isometrically into a Banach space Y , then Y contains an isometric linear copy of X. This is false for every nonseparable weakly compactly generated Banach space X. Canonical examples of nonseparable Banach spaces which are Lipsch...

A Banach space has property (S) if every normalized weakly null sequence contains a subsequence equivalent to the unit vector basis of c0. We show that the equivalence constant can be chosen "uniformly", i.e., independent of the choice of the normalized weakly null sequence. Furthermore we show that a Banach space with property (S) has property (u). This solves in the negative the conjecture th...

We prove a structural property of the class of unconditionally saturated separable Banach spaces. We show, in particular, that for every analytic set A, in the Effros-Borel space of subspaces of C[0, 1], of unconditionally saturated separable Banach spaces, there exists an unconditionally saturated Banach space Y , with a Schauder basis, that contains isomorphic copies of every space X in the c...

Abstract. We prove that if X is a separable infinite dimensional Banach space then its isomorphism class has infinite diameter with respect to the Banach-Mazur distance. One step in the proof is to show that if X is elastic then X contains an isomorph of c0. We call X elastic if for some K <∞ for every Banach space Y which embeds into X, the space Y is K-isomorphic to a subspace of X. We also p...

We show that any separable stable Banach space can be represented as a group of isometries on a separable reflexive Banach space, which extends a result of S. Guerre and M. Levy. As a consequence, we can then represent homeomorphically its space of types.