SPECTRAL ANALYSIS OF COLLECTIVELY COMPACT, STRONGLY CONVERGENT OPERATOR SEQUENCES.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1967
- Accession Number
- AD0657568
Entities
People
- P. M. Anselone
- T. W. Palmer
Organizations
- University of Wisconsin–Madison