保持算子束部分等距的映射

数学物理学报 ›› 2016, Vol. 36 ›› Issue (3): 413-424.

保持算子束部分等距的映射

卫雅楠, 吉国兴

陕西师范大学数学与信息科学学院西安 710119

收稿日期:2015-11-16 修回日期:2016-04-12 出版日期:2016-06-26 发布日期:2016-06-26
通讯作者: 吉国兴 E-mail:gxji@snnu.edu.cn
作者简介:卫雅楠,weiyanan1007@163.com;
基金资助:
国家自然科学基金（11371233）和中央高校基本科研业务费专项资金（GK201301007）资助

Maps Preserving Partial Isometries of Operator Pencils

Wei Yanan, Ji Guoxing

College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119

Received:2015-11-16 Revised:2016-04-12 Online:2016-06-26 Published:2016-06-26
Supported by:
Supported by the NSFC (11371233) and the Fundamental Research Funds for the Central Universities (GK201301007)

摘要/Abstract

摘要：

设B(H)是复Hilbert空间H上的有界线性算子全体，PI(H)表示B(H)中全体部分等距的集合. 该文证明了B(H)上的满射Φ保持算子束(pencil)部分等距，即A-λB∈PI(H)⇔Φ()-λΦ(B)∈PI(H)的充要条件是存在H上的两个酉算子U，V使得对于任意的X∈B(H)都有Φ(X)=UXV或存在H上的两个共轭酉算子U，V使得对于任意的X∈B(H)都有Φ(X)=UX^*V.

关键词: 部分等距, 偏序, 满射, 算子束

Abstract:

Let B(H) be the algebra of all bounded linear operators on a complex Hilbert space H, PI(H) the set of all partial isometries in B(H). It is proved that a surjective map Φ on B(H) preserves partial isometries of pencils of operators, that is, A-λB∈PI(H)⇔Φ(A)-λΦ(B)∈PI(H) if and only if there are two unitary operators U and V on H such that Φ(X)=UXV for all X in B(H) or there are two anti-unitary operators U and V on H such that Φ(X)=UX^*V for all X in B(H).

Key words: Partial isometry, Partial ordering, Surjective map, Operator pencil

中图分类号:

O177.1

卫雅楠, 吉国兴. 保持算子束部分等距的映射[J]. 数学物理学报, 2016, 36(3): 413-424.

Wei Yanan, Ji Guoxing. Maps Preserving Partial Isometries of Operator Pencils[J]. Acta mathematica scientia,Series A, 2016, 36(3): 413-424.

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