5 papers · 1 filter
Applications of the quantification of super weak compactness
Guillaume Grelier, Matías Raja
We introduce a measure of super weak noncompactness defined for bounded linear operators and subsets in Banach spaces that allows to state and prove a characterization of the B…
On uniformly convex functions
Guillaume Grelier, Matías Raja
Non-convex functions that yet satisfy a condition of uniform convexity for non-close points can arise in discrete constructions. We prove that this sort of discrete uniform convexi…
Uniformly convex renormings and generalized cotypes
Luis C. García-Lirola, Matías Raja
We are concerned about improvements of the modulus of convexity by renormings of a super-reflexive Banach space. Typically optimal results are beyond Pisier's power functions bound…
On strong asymptotic uniform smoothness and convexity
Luis García-Lirola, Matías Raja
We introduce the notions of strong asymptotic uniform smoothness and convexity. We show that the injective tensor product of strongly asymptotically uniformly smooth spaces is asym…
A Bourgain-like property of Banach spaces with no copies of
A. Pérez, M. Raja
We give a characterization of the existence of copies of in Banach spaces in terms of indexes. As an application, we deduce new proofs of James Distortion theorem and Bessa…