Document Type



Mathematics (Pomona)

Publication Date



Complex symmetric operator, operator norm, triangle inequality, selfadjoint operator, Cartesian decomposition, approximate antilinear eigenvalue problem, antilinear, spectrum


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 self-adjoint operators Re T and Im T, 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.


First published in Proceedings of the American Mathematical Society in Volume 136, Number 1, January 2008, published by the American Mathematical Society.

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© 2007 American Mathematical Society

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