On the classification of Lindenstrauss spaces
H. Elton Lacey · Pacific Journal of Mathematics · 1973
A Lindenstrauss space is a real Banach space X such that its dual X* is linearly isometric to Li(β) for some measure μ.The purpose of this paper is to describe how certain classical types of Lindenstrauss spaces are characterized by mappings from a compact Hausdorff space S into C(S)*.Let S be a compact Hausdorff space and p: S->C(S)* a bounded function such that for each feC(S), the function f p defined by fp( s ) -\fdp(s) is integrable with respect to each regular Borel measure on S. Thus p induces a natural bounded linear operator P on C(S)* defined by (Pμ)(f) = \f P dμ for all μeC(S)* and/eC(S).