Automatic continuity of biorthogonality preservers between weakly compact JB$^*$-triples and atomic JBW$^*$-triples
Operator Algebras
2024-02-02 v1 Functional Analysis
Abstract
We prove that every biorthogonality preserving linear surjection from a weakly compact JBtriple containing no infinite dimensional rank-one summands onto another JB-triple is automatically continuous. We also show that every biorthogonality preserving linear surjection between atomic JBWtriples containing no infinite dimensional rank-one summands is automatically continuous. Consequently, two atomic JBW-triples containing no rank-one summands are isomorphic if, and only if, there exists a (non necessarily continuous) biorthogonality preserving linear surjection between them.
Cite
@article{arxiv.2402.00517,
title = {Automatic continuity of biorthogonality preservers between weakly compact JB$^*$-triples and atomic JBW$^*$-triples},
author = {María Burgos and Jorge J. Garcés and Antonio M. Peralta},
journal= {arXiv preprint arXiv:2402.00517},
year = {2024}
}