Some matrix transformations on analytic sequence spaces

Tom (Roy Thomas Jr.) Jacob

Vol. 59 (1975), No. 2, 487–491

DOI: 10.2140/pjm.1975.59.487

Abstract

Let A denote the space of all complex sequences a such that if z is a complex number and |z| < 1 then ∑ a_nzⁿ converges, and B the space of all complex sequences b for which there is a complex number z such that |z| > 1 and ∑ b_nzⁿ converges. In this paper we characterize matrix transformations from A to B and from B to A.

Mathematical Subject Classification 2000

Primary: 40C05

Milestones

Received: 23 January 1975

Revised: 22 July 1975

Published: 1 August 1975