Accession Number : AD0697062

Title :   RANGE-DOMAIN IMPLICATIONS FOR CONCAVE OPERATORS,

Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

Personal Author(s) : Schroder,Johann

Report Date : OCT 1969

Pagination or Media Count : 28

Abstract : Let R and S denote linear spaces and M:R(arrow)S an operator which is concave in some rather general sense. Sufficient conditions are derived such that an element u epsilon B included in R belongs to a certain set K included in R whenever Mu is contained in some given set C included in S. Results of an earlier paper on linear operators are generalized in different ways. For example, the set K may have empty interior. There is also given a generalization of the matrix class M of Fiedler and Ptak. Some examples are concerned with operators in the Hilbert Space l sub 2. (Author)

Descriptors :   (*OPERATORS(MATHEMATICS), SET THEORY), CONVEX SETS, TOPOLOGY, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE