Proceedings of the Centre for Mathematics and its Applications

Contractive projections on Banach spaces

Abstract

Increasing sequences of contractive projections on a reflexive $L^p$ space share an unconditionality property similar to that exhibited sequences of self-adjoint projections on a Hilbert space. A slight variation of this property is shown to be precisely the correct condition on a reflexive Banach space to ensure that every operator with a contractive $AC$-functional calculus is scalar-type spectral.

Article information

Dates
First available in Project Euclid: 18 November 2014