On norm-preserving isomorphisms of L-p (mu, H)
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.45, no.1, pp.33-41, 2016 (SCI-Expanded, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 45 Issue: 1
- Publication Date: 2016
- Doi Number: 10.15672/hjms.20164512488
- Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
- Page Numbers: pp.33-41
- Süleyman Demirel University Affiliated: Yes
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.