On the Birman-Krein Theorem

被引：1
|
作者：
Bazao, Vanderlea R. [1 ]
de Oliveira, Cesar R. [2 ]
Diaz, Pablo A. [2 ]
机构：
[1] UFGD, Fac Ciencias Exatas & Tecnol, BR-79804970 Dourados, MS, Brazil
[2] Univ Fed Sao Carlos, Dept Matemat, BR-13560970 Sao Carlos, SP, Brazil
来源：
COMPTES RENDUS MATHEMATIQUE | 2023年 / 361卷 / 01期
关键词：
D O I：
10.5802/crmath.473
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is shown that if X is a unitary operator so that a singular subspace of U is unitarily equivalent to a singular subspace of UX (or XU), for each unitary operator U, then X is the identity operator. In other words, there is no nontrivial generalization of Birman-Krein Theorem that includes the preservation of a singular spectral subspace in this context.
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页码：1081 / 1086
页数：6
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