In this paper, the σ_duals of two classes important sequence spaces l 1(X) and l ∞(X) are investigated, and shows that some topology properties of locally convex space (X,τ) can be characterized by the σ _dua...In this paper, the σ_duals of two classes important sequence spaces l 1(X) and l ∞(X) are investigated, and shows that some topology properties of locally convex space (X,τ) can be characterized by the σ _duals. The criterions of bounded sets in l 1(X) and l ∞(X ) with respect to the weak topologies generated by the σ _duals are obtained. Furthermore, a Schur type result and an automatic continuity theorem of matrix transformation are established.展开更多
文摘In this paper, the σ_duals of two classes important sequence spaces l 1(X) and l ∞(X) are investigated, and shows that some topology properties of locally convex space (X,τ) can be characterized by the σ _duals. The criterions of bounded sets in l 1(X) and l ∞(X ) with respect to the weak topologies generated by the σ _duals are obtained. Furthermore, a Schur type result and an automatic continuity theorem of matrix transformation are established.
基金supported by NSFC(No.11271043,No.11471186)NSF of Beijing(No.1162002)the postdoctoral research foundation of Capital Normal University(No.043175606800/021)
