A Note on Aluthge Transforms of Complex Symmetric Operators and Applications

Article

DOI: 10.1007/s00020-009-1719-5

Cite this article as:
Wang, X. & Gao, Z. Integr. equ. oper. theory (2009) 65: 573. doi:10.1007/s00020-009-1719-5

Abstract.

In this paper, we reprove that: (i) the Aluthge transform of a complex symmetric operator \(\tilde{T} = |T|^{\frac{1}{2}} U|T|^{\frac{1}{2}}\) is complex symmetric, (ii) if T is a complex symmetric operator, then \((\tilde{T})^{*}\) and \(\widetilde{T^{*}}\) are unitarily equivalent. And we also prove that: (iii) if T is a complex symmetric operator, then \(\widetilde{(T^{*})}_{s,t}\) and \((\tilde{T}_{t,s})^{*}\) are unitarily equivalent for s, t > 0, (iv) if a complex symmetric operator T belongs to class wA(t, t), then T is normal.

Mathematics Subject Classification (2000).

Primary 47A05 Secondary 47B20 

Keywords.

Complex symmetric operator Aluthge transform unitary equivalence normal operator p-hyponormal operator class wA(s, tw-hyponormal operator 

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.LMIB and Department of MathematicsBeihang UniversityBeijingChina

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