# Accession Number:

## AD0292918

# Title:

## MATRICES OF LINEAR OPERATORS

# Descriptive Note:

# Corporate Author:

## WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1962-11-01

# Pagination or Media Count:

## 1.0

# Abstract:

The classical Hamilton-Cayley theorem is extended as follows to matrices of operators on a Banach space B. Let a sub ij I K sub ij , i,j 1,..., m, where the a sub ij are scalars, I is the identity operator on B, and the K sub ij are compact linear operators on B. Let Plambda be the characteristic polynomial of a sub ij . Then P represents a compact operator on the product space B-m. This theorem is applied to the study of the asymptotic behavior of a sequence of elements in B which satisfy a composite recusion formula. In addition, the theorem is generalized to an abstract algebraic setting. Author