Resumen de The b-Gelfand–Phillips property for locally convex spaces

Taras Banakh, Saak S. Gabriyelyan

• We extend the well-known Gelfand–Phillips property for Banach spaces to locally convex spaces, defining a locally convex space E to be b-Gelfand–Phillips if every limited set in E, which is bounded in the strong topology on E, is precompact in Several characterizations of b-Gelfand–Phillips spaces are given. The problem of preservation of the b-Gelfand–Phillips property by standard operations over locally convex spaces is considered. Also we explore the b-Gelfand–Phillips property in spaces C(X) of continuous functions on a Tychonoff space X. If and are two locally convex topologies on C(X) such that where is the topology of pointwise convergence and is the compact-open topology on C(X), then the b-Gelfand–Phillips property of the function space implies the b-Gelfand–Phillips property of If additionally X is metrizable, then the function space is b-Gelfand–Phillips.