Geometry of Function Spaces

Abstract

In recent years the use of the techniques from the geometric theory of Banach spaces in the study of function spaces has become an important tool and we are happy that this special issue has received the attention of both senior and young researchers in these areas. We have received papers from a wide cross-section of researchers in this area, covering existence theorems concerning the convolution of functions, distributions, and ultradistributions of Beurling type with supports satisfying suitable compatibility conditions and the Rayleigh equation of two deviating arguments. Application of the Leray-Schauder index theorem and the Leray-Schauder fixed point theorem towards the existence of nontrivial periodic solutions of this type of equations is covered. Also covered is smooth approximation of Lipschitz functions on Finsler manifolds, keeping control on the corresponding Lipschitz constants. An article that extends the usual notion ofKothe dual of a Banach function space to a broad class of Banach lattices is also in this collection. On abstract Banach space theory, there is an article that studies a weakening of the notion of central subspace of a Banach space, as well as an article that studies notions of generalized approximation properties.