Beyond the minimax principle
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- by Chandler Davis PDF
- Proc. Amer. Math. Soc. 81 (1981), 401-405 Request permission
Abstract:
Let $A$ be selfadjoint and $P$ an orthoprojector. Then for any real $\lambda$, the compression of $A$ to the subspace $P\mathcal {H}$ has spectral projector belonging to $]\lambda$, $\infty [$ no larger in dimensionality than does $A$. This generalizes the classical Poincaré inequality. Several other like generalizations are given of various versions of the "minimax principle".References
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I. C. Gohberg and M. G. Kreǐn, Introduction to the theory of linear non-selfadjoint operators, Izdat. "Nauka", Moscow, 1965; English transl., Transl. Math. Monographs, vol. 18, Amer. Math. Soc., Providence, R. I., 1969.
- Hans F. Weinberger, Variational methods for eigenvalue approximation, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 15, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1974. Based on a series of lectures presented at the NSF-CBMS Regional Conference on Approximation of Eigenvalues of Differential Operators, Vanderbilt University, Nashville, Tenn., June 26–30, 1972. MR 0400004
- Alexander Weinstein and William Stenger, Methods of intermediate problems for eigenvalues, Mathematics in Science and Engineering, Vol. 89, Academic Press, New York-London, 1972. Theory and ramifications. MR 0477971
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 401-405
- MSC: Primary 47A10; Secondary 47A20
- DOI: https://doi.org/10.1090/S0002-9939-1981-0597650-7
- MathSciNet review: 597650