Boolean valued analysis and type I \(AW^*\)-algebras
type: Item
instance of: scholarly article
title: Boolean valued analysis and type I \(AW^*\)-algebras
zbMATH Open document ID: 0581.46047
author: Masanao Ozawa
published in: Proceedings of the Japan Academy. Series A
publication date: 1983-01-01T00:00:00Z
review text: This note is in answer to the question raised by \textit{I. Kaplansky} [Ann. Math., II. Ser. 56, 460-472 (1952; Zbl 0047.357)] whether there is a unique cardinal number attached to a homogeneous \(AW^*\)-algebra of type I. The answer is negative as initially conjectured by him [Am. J. Math. 75, 839-858 (1953; Zbl 0051.091)]. The detailed proof of the result will be published by the author in a latter paper. The method is by way of Boolean valued analysis as developed by Takeuti and Ozawa recently.
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 03C90
Mathematics Subject Classification ID: 46L35
zbMATH DE Number: 3929723
zbMATH Keywords: homogeneous \(AW^*\)-algebra of type I
zbMATH Keywords: Boolean valued analysis
reviewed by: M. K. Nayak
MaRDI profile type: Publication
full work available at URL: pjaa.59.368
OpenAlex ID: W2069851367
cites work: Q5652808
cites work: Q3852172
cites work: Algebras of type I
cites work: Modules Over Operator Algebras
cites work: Boolean valued interpretation of Hilbert space theory
cites work: A classification of type I \(AW^*\)-algebras and Boolean valued analysis
cites work: Two Applications of Logic to Mathematics
cites work: A transfer principle in harmonic analysis
cites work: Von Neumann algebras and Boolean valued analysis
cites work: Q5676214
DOI: 10.3792/PJAA.59.368
description: scientific article; zbMATH DE number 3929723