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

• Autorzy: María Burgos , Jorge J. Garcés , Antonio M. Peralta
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46L70: Nonassociative selfadjoint operator algebras
• 46L05: General theory of C * -algebras
• 47B49: Transformers, preservers (operators on spaces of operators)
• 46K70: Nonassociative topological algebras with an involution
• 17A40: Ternary compositions
• 46L40: Automorphisms
• 17C65: Jordan structures on Banach spaces and algebras
• 47B47: Commutators, derivations, elementary operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 204
• Numer: 2
• Strony: 97-121

Daty

wydano

2011

Twórcy

autor

María Burgos

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

autor

Jorge J. Garcés

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

autor

Antonio M. Peralta

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Identyfikatory

DOI

10.4064/sm204-2-1