Let X be a locally convex space and X~* its dual space.Let N(X) denote a localbase neighborhoods 0∈X which are barrells.For each U∈N(X),letP_U(x)=sup{|f(x)|:f∈U^0}, (?)x∈X,where U^0 is polar of U with respect to the dual pair (X, X~*).Then P_U is a continuousseminorm on X. Pietsch gave the vector-valued sequence space l_1[X] as follows:
<正> Termonology used in this paper is the same as in paper[1].Let Λbe a perfect sequence space with μ-topology and E a locally convex space.Thevector-valued sequence space Λ(E)and the topology Γ_πon Λ(E)are defined in[1].Through-out this paper,Let Λ~x have the strong topology β(Λ~x,Λ)and E~* have the strong~*
