Multiplication operators and composition operators on Orlicz spaces
by
B.S. Komal
Department of Mathematics,University of Jammu,Jammu-180004,India
Coauthors: Shally Gupta

Let X and Y be two non empty sets and let F(X) and F(Y) be two topological vector spaces of complex valued functios on X and Y respectively.If T:Y- > X is a mapping such that foT is an element of F(Y) whenever f is an element of F(X), then we can define a composition transformation CT;F(X)-F(Y) by CT(f) =foT for every f in F(X).In case CT happens to be bounded it is known as composition operator.Let u;X-> C be a complex valued function. Then the continuous linear operator Mu :F(X)->F(X) defined by by Mu(f) = u.f is called a Multiplication operator.The multiplication operators and composition operators have been the subject matter of study over the last two decades on different function spaces.In this paper we initiated a study of these operators on Orlicz spaces. The Orlicz spaces are considered as the generalisations of Lp spaces.The compact, Fredholm, isometric and invertible multiplication as well as composition operators on Orlicz spaces are characterised.The invariant subspaces of these operators in some cases are obtained.Some properties of Frobenius - Perron operators are studied in the end of the paper.

Date received: July 26, 2003