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
This paper presents the popularization of the weighting of Chebyshev's inequality and discusses the relation between this popularization and some famous inequalities.
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.
文摘This paper presents the popularization of the weighting of Chebyshev's inequality and discusses the relation between this popularization and some famous inequalities.
