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

Jinghao Huang; Fedor Sukochev

doi:10.1016/j.jfa.2021.108994

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

Functional Analysis 2022-08-29 v6

Authors: Jinghao Huang , Fedor Sukochev

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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.

Keywords

isomorphic classification lpq spaces sigma-finite measure space resonant measure space subspaces

Cite

@article{arxiv.2008.11399,
  title  = {Isomorphic classification of $L_{p,q}$-spaces, II},
  author = {Jinghao Huang and Fedor Sukochev},
  journal= {arXiv preprint arXiv:2008.11399},
  year   = {2022}
}

Comments

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

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

Abstract

Keywords

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