Factorization in analytic crossed products

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概要

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• Let M be a von Neumann algebra, let α be a *-automorphism of M, and let M\rtimes<SUB>α</SUB>\bm{Z} be the crossed product determined by M and α. In this paper, considering the Cholesky decomposition for a positive operator in M\rtimes<SUB>α</SUB>\bm{Z}, we give a factorization theorem for positive operators in M\rtimes<SUB>α</SUB>\bm{Z} with respect to analytic crossed product M\rtimes<SUB>α</SUB>\bm{Z}<SUB>+</SUB> determined by M and α. And we give a necessary and sufficient condition that every positive operator in M\rtimes<SUB>α</SUB>\bm{Z} can be factored by the form A<SUP>*</SUP>A, where A belongs to M\rtimes<SUB>α</SUB>\bm{Z}<SUB>+</SUB>∩(M\rtimes<SUB>α</SUB>\bm{Z}<SUB>+</SUB>)<SUP>-1</SUP>.

• 社団法人 日本数学会の論文

著者

• Saito Kichi-suke

  Department Of Mathematics Faculty Of Science Niigata University

• OHWADA Tomoyoshi

  Department of Mathematics General Education Tsuruoka National college of Technology

関連論文

• Factorization in analytic crossed products
• Certain invariant subspace structure of analytic crossed products
• Equivalence Classes of Invariant Subspaces in Nonselfadjoint Crossed Products
• Nonselfadjoint crossed products II

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