Variational Principles for Symmetric Bilinear Forms

Authors

Jeffrey Danciger, Stanford University
Stephan Ramon Garcia, Pomona CollegeFollow
Mihai Putinar, University of California - Santa Barbara

Document Type

Article

Department

Mathematics (Pomona)

Publication Date

2008

Keywords

Symmetric bilinear form, Friedrichs operator, singular values, compact operator, compressed Toeplitz operator, Courant principle, minimax theorem

Abstract

Every compact symmetric bilinear form B on a complex Hilbert space produces, via an antilinear representing operator, a real spectrum consisting of a sequence decreasing to zero. We show that the most natural analog of Courant's minimax principle for B detects only the evenly indexed eigenvalues in this spectrum. We explain this phenomenon, analyze the extremal objects, and apply this general framework to the Friedrichs operator of a planar domain and to Toeplitz operators and their compressions.

Rights Information

© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1002/mana.200510641

Recommended Citation

Danciger, J., Garcia, S. R. and Putinar, M. (2008), Variational principles for symmetric bilinear forms. Math. Nachr., 281: 786–802. doi: 10.1002/mana.200510641