Accession Number : AD0657568

Title :   SPECTRAL ANALYSIS OF COLLECTIVELY COMPACT, STRONGLY CONVERGENT OPERATOR SEQUENCES.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Anselone,P. M. ; Palmer,T. W.

Report Date : APR 1967

Pagination or Media Count : 17

Abstract : 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 f(T) is defined by the operational calculus, then f(Tn) is eventually defined, f(Tn) approaches f(T) strongly, and (f(Tn) - f(T)) is collectively compact. If f(Tn) and f(T) are spectral projections, the corresponding structural subspaces eventually have the same dimension. Other results compare eigenvalues and generalized eigenmanifolds of Tn and T. (Author)

Descriptors :   (*OPERATORS(MATHEMATICS), BANACH SPACE), ANALYTIC FUNCTIONS, CONVERGENCE, INTEGRAL EQUATIONS, MAPPING(TRANSFORMATIONS), HILBERT SPACE, INEQUALITIES, THEOREMS, VECTOR SPACES

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE