Weak Operator Topology, Operator Ranges and Operator Equations via Kolmogorov Widths

摘要

Let K be an absolutely convex infinite-dimensional compact in a Banach space chi. The set of all bounded linear operators T on chi satisfying TK superset of K is denoted by G(K). Our starting point is the study of the closure WG(K) of G(K) in the weak operator topology. We prove that WG(K) contains the algebra of all operators leaving <(lin(K))over bar> invariant. More precise results are obtained in terms of the Kolmogorov n-widths of the compact K. The obtained results are used in the study of operator ranges and operator equations.