Convergence theorems in Banach algebras

Robert Beauwens and Jean-Jacques Van Binnebeek

Vol. 68 (1977), No. 1, 13–24

DOI: 10.2140/pjm.1977.68.13

Abstract

It is shown that several convergence theorems for linear operators, usually established by Hilbert space techniques are consequences of the general relations between convergence, monotonicity and order units in ordered Banach spaces.

Mathematical Subject Classification 2000

Primary: 46H05

Milestones

Received: 3 June 1975

Published: 1 January 1977