Title

The Eigenstructure of Complex Symmetric Operators

Document Type

Book Chapter

Department

Mathematics (Pomona)

Publication Date

2008

Keywords

Complex symmetric operator, bilinear form, Toeplitz matrix, Hankel operator, Riesz idempotent, Resz basis, generalized eigenvectors

Abstract

We discuss several algebraic and analytic aspects of the eigenstructure (si.e., eigenvalues, eigenvectors, and generalized eigenvectors) of complex symmetric operators. In particular, we examine the relationship between the bilinear form [x,y] = induced by a conjugation C on a complex Hilbert space H and the eigenstructure of a bounded linear operator T: H → H which is C-symmetric (T = CT*C).

Rights Information

© 2008 Springer-Verlag

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