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

María Burgos; Jorge J. Garcés; Antonio M. Peralta

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

María Burgos; Jorge J. Garcés; Antonio M. Peralta

Studia Mathematica (2011)

Volume: 204, Issue: 2, page 97-121
ISSN: 0039-3223

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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 (not necessarily continuous) biorthogonality preserving linear surjection between them.

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María Burgos, Jorge J. Garcés, and Antonio M. Peralta. "Automatic continuity of biorthogonality preservers between weakly compact JB*-triples and atomic JBW*-triples." Studia Mathematica 204.2 (2011): 97-121. <http://eudml.org/doc/285624>.

@article{MaríaBurgos2011,
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 (not necessarily continuous) biorthogonality preserving linear surjection between them.},
author = {María Burgos, Jorge J. Garcés, Antonio M. Peralta},
journal = {Studia Mathematica},
keywords = {weakly compact JB*-triple; automatic continuity; biorthogonality preserver},
language = {eng},
number = {2},
pages = {97-121},
title = {Automatic continuity of biorthogonality preservers between weakly compact JB*-triples and atomic JBW*-triples},
url = {http://eudml.org/doc/285624},
volume = {204},
year = {2011},
}

TY - JOUR
AU - María Burgos
AU - Jorge J. Garcés
AU - Antonio M. Peralta
TI - Automatic continuity of biorthogonality preservers between weakly compact JB*-triples and atomic JBW*-triples
JO - Studia Mathematica
PY - 2011
VL - 204
IS - 2
SP - 97
EP - 121
AB - 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 (not necessarily continuous) biorthogonality preserving linear surjection between them.
LA - eng
KW - weakly compact JB*-triple; automatic continuity; biorthogonality preserver
UR - http://eudml.org/doc/285624
ER -

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