Variational principles for symmetric bilinear forms |
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| Authors: | Jeffrey Danciger Stephan Ramon Garcia Mihai Putinar |
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| Institution: | 1. Department of Mathematics, Building 380, Stanford University, Stanford, CA 94305, USA;2. Phone: +1 818 642 3618, Fax: +1 650 725 4066;3. Department of Mathematics, 610 N. College Ave., Pomona College, Claremont, CA 91711, USA;4. Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California, 93106‐3080, USA;5. Phone: +1 805 893 3252, Fax: +1 805 893 2385 |
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| 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. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Symmetric bilinear form Friedrichs operator singular values compact operator compressed Toeplitz operator Courant principle minimax theorem |
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