Remarks on separation of convex sets, fixed-point theorem, and applications in theory of linear operators

Soltanov K. N.

FIXED POINT THEORY AND APPLICATIONS, 2007 (SCI-Expanded) identifier identifier


Some properties of the linear continuous operator and separation of convex subsets are investigated in this paper and a dual space for a subspace of a reflexive Banach space with a strictly convex norm is constructed. Here also an existence theorem and fixed-point theorem for general mappings are obtained. Moreover, certain remarks on the problem of existence of invariant subspaces of a linear continuous operator are given.