The Eigenstructure of Complex Symmetric Operators

Authors

Stephan Ramon Garcia, Pomona CollegeFollow

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

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1007/978-3-7643-8539-2_10

Recommended Citation

Garcia, S.R., The eigenstructure of complex symmetric operators, Operator Theory: Advances and Applications 179 (2008), 169-184. MR2397854 (2009e:47004) doi: 10.1007/978-3-7643-8539-2_10