In 1996, it was published the seminal work of Rochberg “Higher order estimates in complex
interpolation theory”(Rochberg, 1996). Among many other things, the paper contains a new …

We prove three new dichotomies for Banach spaces à la WT Gowers' dichotomies. The three
dichotomies characterise respectively the spaces having no minimal subspaces, having no …

We provide three new examples of twisted Hilbert spaces by considering properties that are"
close" to Hilbert. We denote them $ Z (\mathcal J) $, $ Z (\mathcal S^ 2) $ and $ Z (\mathcal …

We establish an index theorem for Toeplitz operators on odd-dimensional spin manifolds
with boundary. It may be thought of as an odd-dimensional analogue of the Atiyah–Patodi …

If a Banach space has an unconditional basis it either contains a continuum of non
isomorphic subspaces or is isomorphic to its square and hyperplanes and satisfies other …

For every $\alpha<\omega_1 $ we establish the existence of a separable Banach space
whose Szlenk index is $\omega^{\alpha\omega+ 1} $ and which is universal for all …

A number of results have surfaced over some years that involve questions about Banach
spaces of the following kind: Suppose E is a Banach space such that every normalised …

This paper complements a recent result of Dilworth, Ferenczi, Kutzarova and Odell
regarding the ergodicity of strongly asymptotic $\ell _p $ spaces. We state this result in a …

We prove that a Schauder frame for any separable Banach space is shrinking if and only if it
has an associated space with a shrinking basis, and that a Schauder frame for any …

We present a topological frame in which it is possible to estimate the complexity of some
Borel families of separable Banach spaces. We use this frame for evaluating the complexity …