关键词: 局部p -凸空间, 赋p -范空间, (赋范)共轭锥, 影子锥, 次表示定理

Abstract:

This paper falls into the category of non-locally convex analysis. In this paper the author deals with the representation problems of the normed conjugate cones (l ^p)_p^* and [L^p(μ)]_p^* of real locally p-convex spaces l ^p and L^p(μ) (0<p< 1), obtains (l ^p)_p*\simeq m⁺×m⁺ and [L^p(μ)]_p^*\simeq M⁺(μ)×M⁺(μ), called the subrepresentation theorems of (l ^p)_p^* and [L^p(μ)]_p^* respectively.

Key words: Locally p-convex space, p-normed space, Normed conjugate cone, Shadow cone, Subrepresentation theorem