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The strong degree of von Neumann algebras and the structure of Lie and Jordan derivations

Published online by Cambridge University Press:  07 September 2004

J. ALAMINOS ,
M. BREšAR  and
A. R. VILLENA
J. ALAMINOS
Affiliation:
Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain. e-mail: alaminos@ugr.esavillena@ugr.es
M. BREšAR
Affiliation:
Department of Mathematics, PF, Koroška 160 University of Maribor, Slovenia. e-mail: bresar@uni-mb.si
A. R. VILLENA
Affiliation:
Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain. e-mail: alaminos@ugr.esavillena@ugr.es
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Abstract

The main theorem states that all Lie and Jordan derivations from a von Neumann algebra $\frak{A}$ into any Banach $\frak{A}$-bimodule are standard. Moreover, this statement is proved for some other classes of algebras. Our approach is based on the algebraic theory of functional identities and the strong degree, and is combined with analytic tools.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 137 , Issue 2 , September 2004 , pp. 441 - 463
Copyright
2004 Cambridge Philosophical Society

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