算子的超不变子空间与Wolf谱

算子的超不变子空间与Wolf谱

徐新军, 纪友清

吉林大学数学学院, 长春 130012

收稿日期:2004-05-08 修回日期:1900-01-01 出版日期:2005-01-26 发布日期:2005-01-20
通讯作者: 徐新军

Hyperinvariant Subspaces and Wolf Spectrum of Operators

XU Xin-jun, JI You-qing

College of Mathematics, Jilin University, Changchun 130012, China

Received:2004-05-08 Revised:1900-01-01 Online:2005-01-26 Published:2005-01-20
Contact: XU Xin-jun

摘要/Abstract

摘要： 对于与Volterra算子V交换的算子T, 通过构造和计算, 证明了：如果f(x)=1是T的一个循环向量, 则A′(V)=A′(T). 因而V的不变子空间都是T的超不变子空间. 此外还证明了T是单的当且仅当T是稠值域的, 进而σ(T)=σ_e(T)=σ_lre(T).

关键词: Volterra算子, 换位, 循环向量, 超不变子空间, 酉自伴, 稠值域, Wolf谱

Abstract: Let T be in the commutant of Volterr a operator V, by construction and calculation, it is proved that if the function f(x)=1 is a cyclic vector of T, then A′(V)=A′(T).Thus all the invariant subspaces of V are hyperinvariant for T. Moreover, it is also proved that if only if ker T=｛0｝ran T=H, σ(T)=σ_e(T)=σ_lre(T).

Key words: Volterra operator, commutant, cyclic vector, hyperinvariant subspace, unitarily self-adjiont, range-dense, Wolf spactrum

中图分类号:

O177.1

徐新军, 纪友清. 算子的超不变子空间与Wolf谱[J]. J4, 2005, 43(01): 29-32.

XU Xin-jun, JI You-qing. Hyperinvariant Subspaces and Wolf Spectrum of Operators[J]. J4, 2005, 43(01): 29-32.