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.
Let the n-pie stationary sequence ξ(t)=(ξ_1(t), …, ξ_n(t))' (t=0, ±1, …) be regular and of full rank, and then-ple the spectral density of stationary sequence N(t)=(N_1(t),…,N_n(t))' (t=0,±1, …) exist. And they are stationarily relative;
