Accession Number : AD0723805

Title :   Some Results on Grothendieck's Condition f double prime for the Approximability of Compact Operators.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Nowosad,Pedro

Report Date : JUL 1970

Pagination or Media Count : 31

Abstract : In this work the author presents a new approach to the problem of approximability of compact linear operators, starting from a form of this problem given by Grothendieck in terms of infinite matrices. This form says that, for matrices P in a certain class, the condition P sup 2 = 0 implies trace of P = 0. The author uses this condition more specifically and resort less to more refined properties of determinants than does Grothendieck. In particular the author is able to enlarge a subclass given by Grothendieck for which the above property on the trace holds and the author formulates new assumptions for its validity in the general case. (Author)

Descriptors :   (*OPERATORS(MATHEMATICS), BANACH SPACE), APPROXIMATION(MATHEMATICS), MATRICES(MATHEMATICS), TOPOLOGY, SEQUENCES(MATHEMATICS), THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE