The Eigenstructure of Complex Symmetric Operators

Document Type

Book Chapter


Mathematics (Pomona)

Publication Date



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


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).

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© 2008 Springer-Verlag

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