Title

Hermitian-Symmetric Inequalities in Hilbert Space

Document Type

Article

Department

Mathematics (Pomona)

Publication Date

2009

Keywords

Complex symmetric operator, complex symmetric matrix, hermitian-symmetric inequalities, hermitian operators, selfadjoint operators, Grunsky inequality, bilinear form

Abstract

We establish several conditions which are equivalent to

|[Bx,x]|≤⟨Ax,x⟩,∀x∈H

, where Ais a nonnegative operator and B is a complex symmetric operator on a separable complex Hilbert space H . Along the way, we also prove a new factorization theorem for complex symmetric operators.

Rights Information

© 2009 Springer-Verlag

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