Isometric classification of the Lp -spaces of infinite dimensional Lebesgue measure

Abstract

We investigate the isometric structure of L p-spaces for the infinite-dimensional Lebesgue measure (RN) Under the continuum hypothesis (CH) we proveL p p(c, L p[0, 1]), where c denotes the cardinality of the continuum, and without CH we obtain an isometric, complemented copy of p(c, L p[0, 1]) inside L p. In a general ramework, we characterize precisely when L p = p(L p[0, 1]) and classify all such isometries.