Continuous operators on paranormed spaces and matrix transformations
Ivor J. Maddox, Michael A. L. Willey · Pacific Journal of Mathematics · 1974
The concept of a paranormed /3-space is defined and some theorems of Banach-Steinhaus type are proved for sequences of continuous linear f unctionals on such a space.For example, necessary and sufficient conditions are given for a sequence (A n (x)) of continuous linear functionals to be in the space of generalized entire sequences, for each x belonging to a paranormed /3-space.The general theorems are then used to characterize matrix transformations between generalized l p spaces and generalized entire sequences.