Factorization in analytic crossed products

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Material Type: 記事
Title: Factorization in analytic crossed products
Author/Editor: Tomoyoshi Ohwada
Kichi-Suke Saito
Author Heading: Tomoyoshi Ohwada
Kichi-Suke Saito
Periodical title: Journal of the Mathematical Society of Japan
No. or year of volume/issue: 54(1) 2002.1
Volume: 54
Issue: 1
Pages: 21～33
Publication date of volume/issue (W3CDTF): 2002-01
ISSN (Periodical Title): 0025-5645
ISSN-L (Periodical Title): 0025-5645
Publication (Periodical Title): Tokyo : Mathematical Society of Japan
Place of Publication (Country Code): JP
Text Language Code: eng
NDLC: ZM31
Target Audience: 一般
Holding library: 国立国会図書館
Call No.: Z53-A209
Data Provider (Database): 国立国会図書館 : 国立国会図書館雑誌記事索引
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Bibliographic ID (NDL): 6080232
http://id.ndl.go.jp/bib/6080232
Bibliographic Record Category (NDL): 632

Summary, etc.: Let M be a von Neumann algebra, let α be a *-automorphism of M, and let M\rtimesα\bm{Z} be the crossed product determined by M and α. In this paper, considering the Cholesky decomposition for a positive operator in M\rtimesα\bm{Z}, we give a factorization theorem for positive operators in M\rtimesα\bm{Z} with respect to analytic crossed product M\rtimesα\bm{Z}+ determined by M and α. And we give a necessary and sufficient condition that every positive operator in M\rtimesα\bm{Z} can be factored by the form A*A, where A belongs to M\rtimesα\bm{Z}+∩(M\rtimesα\bm{Z}+)-1.
DOI: 10.2969/jmsj/1191593953
Access Restrictions: インターネット公開
Data Provider (Database): 科学技術振興機構 : J-STAGE
http://www.jstage.jst.go.jp

Summary, etc.: Let M be a von Neumann algebra, let α be a *-automorphism of M, and let M\rtimesα\bm{Z} be the crossed product determined by M and α. In this paper, considering the Cholesky decomposition for a positive operator in M\rtimesα\bm{Z}, we give a factorization theorem for positive operators in M\rtimesα\bm{Z} with respect to analytic crossed product M\rtimesα\bm{Z}+ determined by M and α. And we give a necessary and sufficient condition that every positive operator in M\rtimesα\bm{Z} can be factored by the form A*A, where A belongs to M\rtimesα\bm{Z}+∩(M\rtimesα\bm{Z}+)-1.
DOI: 10.2969/jmsj/1191593953
https://doi.org/10.2969/jmsj/1191593953
Access Restrictions: インターネット公開
Related Material (URI): http://hdl.handle.net/10191/5689
https://niigata-u.repo.nii.ac.jp/records/2087
http://id.ndl.go.jp/bib/6080232
https://ndlsearch.ndl.go.jp/books/R000000004-I6080232
Data Provider (Database): 国立情報学研究所 : CiNii Research
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CiNii Articles
Bibliographic ID (NDL): 6080232
http://id.ndl.go.jp/bib/6080232
NAID: 10007767453