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The Eigenstructure of Complex Symmetric Operators

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Part of the Operator Theory: Advances and Applications book series (OT,volume 179)

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).

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Mathematics Subject Classification (2000)

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Garcia, S.R. (2007). The Eigenstructure of Complex Symmetric Operators. In: Ball, J.A., Eidelman, Y., Helton, J.W., Olshevsky, V., Rovnyak, J. (eds) Recent Advances in Matrix and Operator Theory. Operator Theory: Advances and Applications, vol 179. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8539-2_10

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