二宽度CSL代数与套代数的因子分解

数学季刊 ›› 2006, Vol. 21 ›› Issue (1): 10-14.

二宽度CSL代数与套代数的因子分解

Department of Mathematical Sciences, Xidian University, Xi'an 710071, China

收稿日期:2003-03-06 出版日期:2006-03-30 发布日期:2023-12-14
作者简介:YANG You-long(1967-),male,native of Iucheng,Shaanxi,an associate professor of Xidian University,Ph.D.,engages in operator theory and system theory;WU Yan(1969-),female,native of Yunyang, Chongqing,a lecturer of Xidian University,engages in operator theory and optimal theory.
基金资助:
Supported by the National Science Foundation of China(90205019)；

Factorization of Width-two CSL Algebras and Nest Algebras

Department of Mathematical Sciences, Xidian University, Xi'an 710071, China

Received:2003-03-06 Online:2006-03-30 Published:2023-12-14
About author:YANG You-long(1967-),male,native of Iucheng,Shaanxi,an associate professor of Xidian University,Ph.D.,engages in operator theory and system theory;WU Yan(1969-),female,native of Yunyang, Chongqing,a lecturer of Xidian University,engages in operator theory and optimal theory.
Supported by:
Supported by the National Science Foundation of China(90205019)；

摘要/Abstract

摘要： In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T=US, where U is unitary and 5 belongs to width-two CSL algebra alg when nest M or N is a countable nest, or S belongs to alg when nests M and N are countable nests. For the factorization of nest,we obtain that T factors as T=US where S∈D^-1_N and U is unitary as N be a countable nest.

关键词: width-two CSL algebra, nest algebra, factorization, invertible operator

Abstract: In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T=US, where U is unitary and 5 belongs to width-two CSL algebra alg when nest M or N is a countable nest, or S belongs to alg when nests M and N are countable nests. For the factorization of nest,we obtain that T factors as T=US where S∈D^-1_N and U is unitary as N be a countable nest.

Key words: width-two CSL algebra, nest algebra, factorization, invertible operator

中图分类号:

O177.1

杨有龙, 吴艳. 二宽度CSL代数与套代数的因子分解[J]. 数学季刊, 2006, 21(1): 10-14.

YANG You-long, WU Yan . Factorization of Width-two CSL Algebras and Nest Algebras[J]. Chinese Quarterly Journal of Mathematics, 2006, 21(1): 10-14.

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