The Eigenstructure of Complex Symmetric Operators

Abstract

We discuss several algebraic and analytic aspects of the eigenstruc-ture (i.e., eigenvalues, eigenvectors, and generalized eigenvectors) of complex symmetric operators. In particular, we examine the relationship between the bilinear form [x, y] = x, Cy 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). Mathematics Subject Classification (2000). 47A05, 47A07, 47A15.