哥氏空間上運算子之弱緊緻性

Abstract

Weak compactness of operators on Grothenaieck spaces is investigated.If Y is a Banach space satisfying one of the following properties : (a)the unit ball of Y* is weak* sequentially compact;(b) Y=C(K) with K a countably compact scattered space; ( c) Y is an L-space; then every bounded linear operator from a Grothendieck space into Y is weakly compact.