In this note, we provide a starlike and normal tiling in any separable Banach space. That means, there are positive constants r R (not depending on the space) such that every tile of is starlike, contains ball radius contained .

We realize the noncommutative Gurarij space NG defined by Oikhberg as the Fräıssé limit of the class of finite-dimensional 1-exact operator spaces. As a consequence we deduce that the noncommutative Gurarij space is unique up to completely isometric isomorphism, homogeneous, and universal among separable 1-exact operator spaces. Moreover we show that NG is isometrically isomorphic to the Gurari...

It is shown that for every closed, convex and nowhere dense subset C of a superreflexive Banach space X there exists a Radon probability measure μ on X so that μ(C + x) = 0 for all x ∈ X. In particular, closed, convex, nowhere dense sets in separable superreflexive Banach spaces are Haar null. This is unlike the situation in separable nonreflexive Banach spaces, where there always exists a clos...

We investigate certain envelopes of open sets in dual Banach spaces which are related to extending holomorphic functions. We give a variety of examples of absolutely convex sets showing that the extension is in many cases not possible. We also establish connections to the study of iterated weak* sequential closures of convex sets in the dual of separable spaces.

In this paper we obtain some strong laws of large numbers (SLLNs) for arrays of rowwise independent (not necessary identically distributed) random compact sets and fuzzy random sets whose underlying spaces are separable Banach spaces. © 2008 Elsevier B.V. All rights reserved.

In this paper two basic random fixed point theorems with PPF dependence are proved for random operators in separable Banach spaces with different domain and range spaces. The obtained abstract results are applied to certain nonlinear functional random differential equations for proving the existence results for random solutions with PPF dependence.

Using the notion of Sξ-strictly singular operator introduced by Androulakis, Dodos, Sirotkin and Troitsky, we define an ordinal index on the subspace of strictly singular operators between two separable Banach spaces. In our main result, we provide a sufficient condition implying that this index is bounded by ω1. In particular, we apply this result to study operators on totally incomparable spa...