Boolean algebras of projections and algebras of spectral operators

H.R. Dowson, M.B. Ghaemi and P.G. Spain

Vol. 209 (2003), No. 1, 1–16

DOI: 10.2140/pjm.2003.209.1

Abstract

We show that, given a weak compactness condition which is always satisfied when the underlying space does not contain an isomorphic copy of c₀, all the operators in the weakly closed algebra generated by the real and imaginary parts of a family of commuting scalar-type spectral operators on a Banach space will again be scalar-type spectral operators, provided that (and this is a necessary condition with even only two operators) the Boolean algebra of projections generated by their resolutions of the identity is uniformly bounded.

Milestones

Received: 1 October 2001

Published: 1 March 2003