Accession Number : AD0292918

Title :   MATRICES OF LINEAR OPERATORS

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : ANSELONE,P.M.

Report Date : NOV 1962

Pagination or Media Count : 1

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 P(lambda) 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)

Descriptors :   *OPERATORS (MATHEMATICS), ALGEBRAS, FUNCTIONAL ANALYSIS, MATHEMATICS, MATRICES(MATHEMATICS), SERIES(MATHEMATICS)

Distribution Statement : APPROVED FOR PUBLIC RELEASE