On Disjointly singular centralizers
Functional Analysis
2019-05-22 v1
Abstract
We study ``disjoint" versions of the notions of trivial, locally trivial, strictly singular and super-strictly singular quasi-linear maps in the context of K\"othe function spaces. Among other results, we show: i) (locally) trivial and (locally) disjointly trivial notions coincide on reflexive spaces; ii) On non-atomic superreflexive K\"othe spaces, no centralizer is singular, although most are disjointly singular. iii) No super singular quasi-linear maps exist between superreflexive spaces although Kalton-Peck centralizers are super disjointly singular; iv) Disjoint singularity does not imply super disjoint singularity.
Cite
@article{arxiv.1905.08241,
title = {On Disjointly singular centralizers},
author = {Jesús M. F. Castillo and Wilson Cuellar and Valentin Ferenczi and Yolanda Moreno},
journal= {arXiv preprint arXiv:1905.08241},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1511.05867