Complex symmetric operators and additive preservers problem
Given a conjugation C on a separable complex Hilbert space H, a bounded linear operator T on H is said to be C-symmetric if \(CTC=T^*\), and is said to be C-skew symmetric if \(CTC=-\,T^*\). In this paper, we provide a complete description of all additive maps, on the algebra of all bounded linear operators acting on H, that preserve C-symmetric operators for every conjugation C. We focus also on the linear maps preserving C-skew symmetric operators.
KeywordsLinear preservers problem Complex symmetric operators Diagonal operators
Mathematics Subject Classification47B49 47B99 47C15
The authors would like to thank the referee for carefully reading our manuscript and making many valuable suggestions which served to improve this paper, especially for drawing our attention to the linear preservers problem of skew-symmetric operators.
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