標題: 滿足Alg T={T}'之線性變換
On Contractions Satisfying Alg T={T}'
作者: 吳培元
P.Y.Wu
公開日期: 四月-1976
出版社: 交大學刊編輯委員會
摘要: For a bound linear operator T on a Hilbert space let {T}', {T}'' and Alg T denote the commutant, the double commutant and the weakly closed algebra generated by T and 1, respectively. Assume that T is a completely non-unitary contrction with a scalar-valued characteristics function Ψ(λ). In this note we show that the condition that |Ψ(e^it)|=1 on a set of positive Lebseque measure implies that Alg T={T}'. Moreover, if Ψ(λ) is assumed to be outer, then these two conditions are equivalent. Our main result generalizes the well-known fact that the compressions of the shift satisfy Alg T={T}'.
URI: http://hdl.handle.net/11536/137545
期刊: 交通大學學報
The Journal of National Chiao Tung University
Volume: 1
起始頁: 263
結束頁: 272
顯示於類別:交通大學學報


文件中的檔案:

  1. HT001307-19.pdf