For a general càdlàg Lévy process X on separable Banach space V we estimate values of inf c≥0 { ψ ( c ) + Y ∈ A

In this note we construct a C∞-smooth, LFC (Locally depending on Finitely many Coordinates) bump function, in every separable Banach space admitting a continuous, LFC bump function.

We construct on any quasi-reflexive of order 1 separable real Banach space an equivalent norm, such that all contractions on the space and all contractions on its dual are mean ergodic, thus answering negatively a question of Louis Sucheston.

A projectional skeleton in a Banach space is a σ-directed family of projections onto separable subspaces, covering the entire space. The class of Banach spaces with projectional skeletons is strictly larger than the class of Plichko spaces (i.e. Banach spaces with a countably norming Markushevich basis). We show that every space with a projectional skeleton has a projectional resolution of the ...

In this paper we study linear into isometries of non-reflexive spaces (embeddings) that preserve finite dimensional structure of the range space. We consider this for various aspects of the finite dimensional structure, covering the recent notion of an almost isometric ideals introduced by Abrahamsen et.al., the well studied notions of a M -ideal and that of an ideal. We show that if a separabl...

Let X and Y be separable Banach spaces. Suppose Y either has a shrinking basis or Y is isomorphic to C(2N) andA is a subset of weakly compact operators from X to Y which is analytic in the strong operator topology. We prove that there is a reflexive space with a basis Z such that every T ∈ A factors through Z. Likewise, we prove that if A ⊂ L(X,C(2N)) is a set of operators whose adjoints have s...

We use Baire categorical arguments to construct dramatically pathological locally Lipschitz functions. The origins of this approach can be traced back to Banach and Mazurkiewicz (1931) who independently used similar categorical arguments to show that \almost every continuous real-valued function deened on 0,1] is nowhere diierentiable". As with the results of Banach and Mazurkiewicz, it appears...