Frechet Differentiable Points in Bochner Function Spaces L p (μ, X)

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. ABSTRACT. In this paper, a characterization of Fr6chet differentiable points of Lp(jI,X), 1 <p < oo, is given: f E Lp(kt,X), f $ 0 is a point of Fr6chet differentiability of the norm if and only if the values f (t) axe such almost everywhere in the support of f.