Vol. 53, No. 1, 1974

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Continuous operators on paranormed spaces and matrix transformations

I. J. Maddox and Michael A. L. Willey

Vol. 53 (1974), No. 1, 217–228

The concept of a paranormed β-space is defined and some theorems of Banach-Steinhaus type are proved for sequences of continuous linear functionals on such a space. For example, necessary and sufficient conditions are given for a sequence (An(x)) of continuous linear functionals to be in the space of generalized entire sequences, for each x belonging to a paranormed β-space. The general theorems are then used to characterize matrix transformations between generalized lp spaces and generalized entire sequences.

Mathematical Subject Classification 2000
Primary: 46A15
Secondary: 40H05
Received: 7 August 1973
Published: 1 July 1974
I. J. Maddox
Michael A. L. Willey