ABSTRACT
In the previous chapters we have focused our attention on some specific classical Banach spaces. In this chapter, we consider a more general class of spaces which includes the Lp-spaces as a special case. Already we have seen a step in that direction in a theorem of Lamperti (mentioned as Theorem 3.5.1 in Chapter 3) which is a partial result for Orlicz spaces. At the suggestion of Lamperti, Lumer extended the result to reflexive Orlicz spaces using a method now referred to as “Lumer’s method” and which has been used extensively by many authors in a variety of settings. This method, first mentioned in the Remarks at the end of Chapter 1, will be prominent in the proofs given in this chapter, and we will develop it fully.
