Abstract:

The author gives a dual characterization of solid cones in locally convex spaces. From this the author obtains some criteria for judging convex cones to be solid in various kinds of locally convex spaces. Using a general expression of the interior of a solid cone, the author obtains a number of necessary and sufficient conditions for convex cones to be solid in the
framework of Banach spaces. In particular, the author gives a dual
relationship between solid cones and generalized sharp cones. The
related known results are improved and extended.

Key words: Convex cones, solid cones, bases of cones, angle property,
locally convex spaces