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.

Authors