Algebras of bounded sequences

Kenneth Myron Hoffman and Arlan Bruce Ramsay

Vol. 15 (1965), No. 4, 1239–1248

DOI: 10.2140/pjm.1965.15.1239

Abstract

Let l^∞ be the algebra of all bounded sequences of complex numbers. The primary purpose of this paper is to settle, by means of a counter-example, a conjecture about subalgebras of l^∞: If A is a subalgebra of l^∞ which is closed under uniform convergence and separates the points of βN, then A = l^∞.

Mathematical Subject Classification

Primary: 46.55

Secondary: 06.60

Milestones

Received: 27 August 1964

Published: 1 December 1965