# 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):

# Report Date:

## 1967-04-01

# Pagination or Media Count:

## 17.0

# 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 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

# Descriptors:

# Subject Categories:

- Theoretical Mathematics