Weights on Jordan Banach algebras
type: Item
instance of: scholarly article
title: Weights on Jordan Banach algebras
zbMATH Open document ID: 0632.46056
DOI: 10.1007/BF01078027
author: A. A. Adizov
publication date: 1987-01-01T00:00:00Z
review text: The main result of the paper is the following Jordanized version of the \textit{U. Haagerup} theorem [J. Funct. Anal. 19, 302-317 (1975; Zbl 0304.46043)] Theorem. Let \(\phi\) be a weight on a JBW-algebra A. The following conditions are equivalent: (1) \(\phi\) is completely additive; (2) \(\phi\) is normal; (3) \(\phi\) is weakly lower semicontinuous; (4) \(\phi (a)=\sup \{\psi (a)\), \(\psi\in F\}\forall a\in A^+\), where F is a family of positive normal functionals; (5) \(\phi (a)=\sum \psi_ i(a)\forall a\in A^+\), where \(\{\psi_ i\}\) is a family of positive normal functionals.
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 46L54
Mathematics Subject Classification ID: 46L70
Mathematics Subject Classification ID: 46L30
zbMATH DE Number: 4028174
zbMATH Keywords: Jordanized version of the Haagerup theorem
zbMATH Keywords: weight on a JBW-algebra
zbMATH Keywords: completely additive
zbMATH Keywords: normal
zbMATH Keywords: weakly lower semicontinuous
zbMATH Keywords: positive normal functionals
reviewed by: Sh. A. Ayupov
MaRDI profile type: Publication
cites work: Normal weights on \(W^*\)-algebras
cites work: Q5565478
cites work: A Gelfand-Neumark theorem for Jordan algebras
cites work: On normed Jordan algebras which are Banach dual spaces
cites work: Semifinite traces on JBW-algebras
cites work: The Radon-Nikodym theorem for weights on semifinite JBW-algebras
cites work: Ideal Theory in JB-Algebras
published in: Functional Analysis and Its Applications
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description: scientific article; zbMATH DE number 4028174