Continuous operators on paranormed spaces and matrix transformations

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

Vol. 53 (1974), No. 1, 217–228

DOI: 10.2140/pjm.1974.53.217

Abstract

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 (A_n(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 l_p spaces and generalized entire sequences.

Mathematical Subject Classification 2000

Primary: 46A15

Secondary: 40H05

Milestones

Received: 7 August 1973

Published: 1 July 1974