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arXiv · 2402.00517

Automatic continuity of biorthogonality preservers between weakly compact JB$^*$-triples and atomic JBW$^*$-triples

María Burgos·Jorge J. Garcés·Antonio M. Peralta
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Abstract

We prove that every biorthogonality preserving linear surjection from a weakly compact JB$^*$triple 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 JBW$^*$triples 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.

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María Burgos, Jorge J. Garcés, Antonio M. Peralta. 2024-02-01. Automatic continuity of biorthogonality preservers between weakly compact JB$^*$-triples and atomic JBW$^*$-triples. https://doi.org/10.4064/sm204-2-1

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