The Eigenstructure of Complex Symmetric Operators.

Authors :: Gohberg, I.
Alpay, D.
Arazy, J.
Atzmon, A.
Ball, J. A.
Ben-Artzi, A.
Bercovici, H.
Böttcher, A.
Clancey, K.
Coburn, L. A.
Curto, R. E.
Davidson, K. R.
Douglas, R. G.
Dijksma, A.
Dym, H.
Fuhrmann, P. A.
Gramsch, B.
Helton, J. A.
Kaashoek, M. A.
Kaper, H. G.
Source :: Recent Advances in Matrix & Operator Theory; 2008, p169-183, 15p
Publication Year :: 2008
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] = <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). [ABSTRACT FROM AUTHOR]