Hermitian liftings in Orlicz sequence spaces

Graham Donald Allen, David Alan Legg and Joseph Dinneen Ward

Vol. 86 (1980), No. 2, 379–387

DOI: 10.2140/pjm.1980.86.379

Abstract

Let M and N be complimentary Orlicz functions satisfying the Δ₂-condition, and let l_M and l_(M) be the Orlicz sequence spaces associated with M with the two usual norms. We show that if 2 is not in the associated interval for M, then every essentially Hermitian operator on l_M or l_(M) is a compact perturbation of a real diagonal operator.

Mathematical Subject Classification 2000

Primary: 47B37

Secondary: 46A45, 46E30, 47B15

Milestones

Received: 2 August 1978

Revised: 8 June 1979

Published: 1 February 1980