Hermitian-Symmetric Inequalities in Hilbert Space

Authors

Stephan Ramon Garcia, Pomona CollegeFollow

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

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1007/s11785-008-0084-8

Recommended Citation

Garcia, S.R., Hermitian-symmetric inequalities in Hilbert space, Complex Anal. Oper. Theory 3 (2009), no. 4, 835–846. MR2570114 (2012a:47039). doi: 10.1007/s11785-008-0084-8