Continuous family of invariant subspaces for R-diagonal operators

• 成果类型: Article
• 署名作者: Sniady, P; Speicher, R
• 署名单位: University of Wroclaw; Queens University - Canada
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220100166
• 发表日期: 2001
• 页码: 329-363
• 关键词: multiplicative functions; ELEMENTS

摘要

We show that every R-diagonal operator x has a continuous family of invariant subspaces relative to the von Neumann algebra generated by x. This allows us to find the Brown measure of x and to find a new conceptual proof that Voiculescu's S-transform is multiplicative. Our considerations base on a new concept of R-diagonality with amalgamation, for which we give several equivalent characterizations.