Isomorphic classification of $L_{p,q}$-spaces, II

Abstract

This is a continuation of the papers [Kuryakov-Sukochev, JFA, 2015] and [Sadovskaya-Sukochev, PAMS, 2018], in which the isomorphic classification of $L_{p,q}$, for $1<p<\infty$, $1\le q<\infty$, $p\ne q$, on resonant measure spaces, has been obtained. The aim of this paper is to give a complete isomorphic classification of $L_{p,q}$-spaces on general $\sigma$-finite measure spaces. Towards this end, several new subspaces of $L_{p,q}(0,1)$ and $L_{p,q}(0,\infty )$ are identified and studied.

details of the proof in theorem 5.7 have been added; Remark 3.4 has been added after this paper was published; fixed an oversight in Corollary 5.8

References in corpus (1)

• Lack of isomorphic embeddings of symmetric function spaces into operator ideals