Quasi-\(WCG\)-spaces (Q1311150)

In the theory of Banach spaces the class of WCG-spaces is well-known, i.e., the spaces \(X\) containing weak compact \(C\) with dense in \(X\) linear span. The class of WCG-spaces includes all reflexive and separable Banach spaces. In the present article we introduce the concept of quasi-WCG- space. In the case of Banach space, this is an analog of a subspace of WCG-space. We show that such a class of spaces includes certain known classes of locally convex spaces and possesses the stability with respect to operations of projective limit and of countable inductive limit. We generalize to quasi-WCG-spaces the known Sobczyk's theorem on extension of operators with values in the space \(c_ 0\).