Aluthge Transforms of Complex Symmetric Operators
Aluthge Transforms of Complex Symmetric Operators
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DOI：
10.1007/s00020-008-1564-y
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发表时间：
2008-02
影响因子：
0.8
通讯作者：
S. Garcia
中科院分区：
文献类型：
--
作者：
S. Garcia
Ifdenotes the polar decomposition of a bounded linear operatorT, then theAluthge transformofTis defined to be the operator. In this note we study the relationship between the Aluthge transform and the class of complex symmetric operators (Tiscomplex symmetricif there exists a conjugate-linear, isometric involutionso thatT=CT*C). In this note we prove that: (1) the Aluthge transform of a complex symmetric operator is complex symmetric, (2) ifTis complex symmetric, thenandare unitarily equivalent, (3) ifTis complex symmetric, thenif and only ifTis normal, (4)if and only ifT2= 0, and (5) every operator which satisfiesT2= 0 is necessarily complex symmetric.
