Interpolation in a Banach space

Weak Interpolation in Banach Spaces

On a Theorem by Lions and Peetre about Interpolation between a Banach Space and Its Dual

We show that if the duality between a Banach space A and its anti-dual A* is given by the inner product of a Hilbert space H, then (A, A*)1/2,2 = H = (A,A*)[l,2~, provided A satisfies certain mild conditions. We do not assume A is reflexive. Applications are given to normed ideals of operators.

Interpolation Functors and Banach Couples

The theory of interpolation spaces originally arose from an attempt to generalize the classical interpolation theorems of M. Riesz and Marcinkiewicz to a more abstract setting. However it should more correctly be described as a theory of "families" of abstract spaces : Given a number of (usually two) spaces contained in a common "large" space, we try to find as many "families" of new such space...

Interpolation of Banach Algebras and Tensor Products of Banach Couples

We consider interpolation of unital Banach algebras, in the special case when the intersection space is non-unital, giving precise conditions of when an interpolation algebra is unital.

Regularity lemmas in a Banach space setting

Szemerédi’s regularity lemma is a fundamental tool in extremal graph theory, theoretical computer science and combinatorial number theory. Lovász and Szegedy [7] gave a Hilbert space interpretation of the lemma and an interpretation in terms of compactness of the space of graph limits. In this paper we prove several compactness results in a Banach space setting, generalising results of Lovász a...