On norm-preserving isomorphisms of L-p (mu, H)


GUNTURK B. A. , Cengiz B., GÜRDAL M.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.45, no.1, pp.33-41, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.15672/hjms.20164512488
  • Title of Journal : HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Page Numbers: pp.33-41

Abstract

Given an arbitrary positive measure space (X, A, mu) and a Hilbert space H. In this article we give a new proof for the characterization theorem of the surjective linear isometries of the space L-p (mu, H) (for 1 <= p < infinity p not equal 2) which is essentially different from the existing one, and depends on the p-projections of L-p (mu, H). We generalize the known characterization of the p-projections of L-p (mu, H) for sigma-finite measure to the arbitrary case. They are proved to be the multiplication operations by the characteristic functions of the locally measurable sets, or that of the clopen (closed-open) subsets of the hyperstonean space the measure mu determines.