Approximate Antilinear Eigenvalue Problems and Related Inequalities
نویسندگان
چکیده
If T is a complex symmetric operator on a separable complex Hilbert space H, then the spectrum σ(|T |) of √ T ∗T can be characterized in terms of a certain approximate antilinear eigenvalue problem. This approach leads to a general inequality (applicable to any bounded operator T : H → H), in terms of the spectra of the selfadjoint operators ReT and ImT , restricting the possible location of elements of σ(|T |). A sharp inequality for the operator norm is produced, and the extremal operators are shown to be complex symmetric.
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