Multinormed semifinite von Neumann algebras, unbounded operators and conditional expectations


Dosi A.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.466, ss.573-608, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 466 Konu: 1
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.jmaa.2018.06.002
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Sayfa Sayıları: ss.573-608

Özet

The present paper is devoted to classification of multinormed W*-algebras in terms of their bounded parts. We obtain a precise description of the bornological predual of a multinormed W*-algebra, which is reduced to a multinormed noncommutative L-1-space in the semifinite case. A multinormed noncommutative L-2-space is obtained as the union space of a commutative domain in a semifinite von Neumann algebra. Multinormed W*-algebras of type I are described as locally bounded decomposable (unbounded) operators associated with a measurable covering. (C) 2018 Elsevier Inc. All rights reserved.