Variational Principles for Symmetric Bilinear Forms

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Mathematics (Pomona)

Publication Date



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


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.

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

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