Vol. 53, No. 1, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Continuous operators on paranormed spaces and matrix transformations

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

Vol. 53 (1974), No. 1, 217–228
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 (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
Milestones
Received: 7 August 1973
Published: 1 July 1974
Authors
I. J. Maddox
Michael A. L. Willey