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Recent Advances in Matrix and Operator Theory pp 169–183Cite as

The Eigenstructure of Complex Symmetric Operators

  • Conference paper

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).

Keywords

  • Complex symmetric operator
  • bilinear form
  • Toeplitz matrix
  • Hankel operator
  • Riesz idempotent
  • Riesz basis
  • generalized eigenvectors.

Mathematics Subject Classification (2000)

  • 47A05
  • 47A07
  • 47A15

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Author information

Authors and Affiliations

  1. Department of Mathematics, Pomona College, 610 North College Avenue, Claremont, CA, 91711, USA

    Stephan Ramon Garcia

Authors
  1. Stephan Ramon Garcia
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061, USA

    Joseph A. Ball

  2. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    Yuli Eidelman

  3. Department of Mathematics, University of California San Diego, 9500 Gilman Drive, La Jolla, California, 92093-0112, USA

    J. William Helton

  4. Department of Mathematics, University of Connecticut, 196 Auditorium Road, U-9, Storrs, CT, 06269, USA

    Vadim Olshevsky

  5. Department of Mathematics, University of Virginia, P. O. Box 400137, Charlottesville, VA, 22904-4137, USA

    James Rovnyak

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Cite this paper

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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