On the Bounded Variation of Operator-Valued Functions

In[1],the Kothe nuclear sequence spaces are described and in[2]the characte-rization of the semi-nuclear and the barreled locally convex spaces by the boundedvariation of functions respectively.In this paper several kinds of bounded variationof operator-valued functions are studied. Let X and Y are Banach spaces,T(t):[0,1]→L(X,Y)be a operator-valued fun-ction.We called T(t)be uniformly bounded variation,if there exist a constantM>0,such that for any partition △:0=t_0