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


GUNTURK B. A. , Cengiz B., GÜRDAL M.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.45, ss.33-41, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 45 Konu: 1
  • Basım Tarihi: 2016
  • Doi Numarası: 10.15672/hjms.20164512488
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Sayfa Sayısı: ss.33-41

Özet

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.