Interpolation in C(Ω)

Benjamin Baxter Wells, Jr.

Vol. 36 (1971), No. 3, 833–838

DOI: 10.2140/pjm.1971.36.833

Abstract

It is known from the work of Bade and Curtis that if A is a Banach subalgebra of C(Ω),Ω a compact Hausdorff space, and if Ω is an F-space in the sense of Gillman and Hendriksen then A = C(Ω). This paper is concerned with the extension of this and similar results to the setting of Grothendieck spaces ( G-spaces for short). An important feature of the extension is that emphasis is shifted from the underlying topological structure of Ω to the linear topological character of C(Ω).

Mathematical Subject Classification

Primary: 46.25

Secondary: 54.00

Milestones

Received: 26 February 1970

Published: 1 March 1971