
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 HamiltonCayley 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 Bm. 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