SPECTRAL ANALYSIS OF COLLECTIVELY COMPACT, STRONGLY CONVERGENT OPERATOR SEQUENCES.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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A set H of operators on a Banach space X is collectively compact iff Kx K epsilon H, Norm x or 1 is precompact. Operators T and T sub n, n or 1, such that T sub n approaches T strongly and Tn -T is collectively compact are investigated. The spectrum of Tn is eventually contained in any given neighborhood of the spectrum of T. If fT is defined by the operational calculus, then fTn is eventually defined, fTn approaches fT strongly, and fTn - fT is collectively compact. If fTn and fT are spectral projections, the corresponding structural subspaces eventually have the same dimension. Other results compare eigenvalues and generalized eigenmanifolds of Tn and T. Author
- Theoretical Mathematics