Characterization of Solid Cones

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 inds 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.