M-ideals in B(l_p)

Roger R. Smith and Joseph Dinneen Ward

Vol. 81 (1979), No. 1, 227–237

DOI: 10.2140/pjm.1979.81.227

Abstract

This paper is concerned with the M-ideal structure of the algebras B(l_p) of bounded operators on the sequence spaces l_p, 1 < p < ∞. The M-summands are completely determined, but the M-ideals are only partially characterized. However evidence is presented to support the conjecture that the only nontrivial M-ideal is the ideal C(l_p) of compact operators on l_p.

Mathematical Subject Classification

Primary: 47D30, 47D30

Secondary: 47B05

Milestones

Received: 22 August 1977

Published: 1 March 1979