Generalized quasi-Banach sequence spaces and measures of noncompactness

We prove a local version of Gowers’ Ramsey-type theorem [21], as well as lo- cal versions both of the Banach space first dichotomy (the “unconditional/HI”.. dichotomy) of Gowers

Given a Banach space X, in [1] the authors introduce a large class of Banach or quasi-Banach spaces formed by X-valued sequences, called invariant sequences spaces, which

Uniform classification of classical Banach spaces.. B¨

We define an ergodic Banach space X as a space such that E 0 Borel reduces to isomorphism on the set of subspaces of X, and show that every Banach space is either ergodic or contains

Gowers therefore produced a list of four inevitable classes of Banach spaces, corresponding to classical examples, or more recent couterexamples to classical questions: HI spaces,

Isomorphism of Banach spaces, Complexity of analytic equivalence relations, Minimal Banach spaces, Spreading models..

Although most of the time we deal with Banach spaces which are in fact quite similar to Hilbert spaces, the natural setting for our study is the category of quasi Banach spaces

This formula, as we shall prove, is in the spirit of Leray-Schauder theory, where the index of an invertible linear compact perturbation of the identity L = I − K is (−1) n , where n