Some properties of homogeneous operator in β-normal linear space
Ni Ren · 2003
The equivalent relation of boundedness and continuity at zero for homogeneous operator in β normal linear space is proved.Let X and Y be two β normal linear spaces and B(X,Y) the set of all bounded homogeneous operators between X and Y.According to the operator norm and linear operation introduced,it is proved that B(X,Y) is a β normal linear space if X is dual separated.It is pointed out that B(X,Y) is complete if and only if the space Y is complete if X is dual separated of bound linear operator in normal linear space.