M-IDEAL PROPERTIES IN ORLICZ-LORENTZ SPACES

Abstract

We provide explicit formulas for the norm of bounded linear functionals on Orlicz-Lorentz function spaces Lambda(phi,omega) equipped with two standard Luxemburg and Orlicz norms. Any bounded linear functional is a sum of regular and singular functionals, and we show that the norm of a singular functional is the same regardless of the norm in the space, while the formulas of the norm of general functionals are different for the Luxemburg and Orlicz norm. The relationship between equivalent definitions of the modular P-phi,P-omega generating the dual space to Orlicz-Lorentz space is discussed in order to compute the norm of a bounded linear functional on Lambda(phi,omega ) equipped with Orlicz norm. As a consequence, we show that the order-continuous subspace of Orlicz-Lorentz space equipped with the Luxemburg norm is an M-ideal in Lambda(phi,omega )while this is not true for the space with the Orlicz norm when phi is an Orlicz N-function not satisfying the appropriate Delta(2) condition. The analogous results on Orlicz-Lorentz sequence spaces are also given.