Matrix transformations involving simple sequence spaces

Tom (Roy Thomas Jr.) Jacob

Vol. 70 (1977), No. 1, 179–187

DOI: 10.2140/pjm.1977.70.179

Abstract

One property of spaces of analytic or entire sequences is that every bounded subset of each of them is contained in the normal hull of a single point of the space. In this paper sequence spaces having this property are studied and many characterizations of matrix transformations involving these spaces and their duals are shown to involve it. Several simple theorems about matrix transformations are proved, and many of the known theorems about matrix transformations on analytic and entire sequences are shown to be special cases of these general theorems.

Mathematical Subject Classification 2000

Primary: 46A45

Milestones

Received: 10 February 1976

Revised: 21 March 1977

Published: 1 May 1977