On compact operators in Orlicz spaces (Q1059255)

\textit{H. P. Rosenthal} [J. Funct. Anal. 4, 176-214 (1969; Zbl 0185.203)] characterized those pairs of spaces \(L_ p(\mu)\), \(L_ r(\nu)\) \((1\leq r<p<\infty)\) for which every bounded linear operator acting from any subspace of \(L_ p(\mu)\) to \(L_ r(\nu)\) is compact. In the work this result is extended to the class composed of reflexive Orlicz function spaces over the interval [0,1] and reflexive Orlicz sequence spaces. For X, Y belonging to the above class the characterisation of complementability of K(X,Y) in L(X,Y) is obtained. L(X,Y) (resp. K(X,Y)) denotes the space of all bounded (resp. compact) operators acting from X to Y. The inequality of Clarkson's type and some other inequalities for norms in reflexive Orlicz spaces are also given.