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Multinormed semifinite von Neumann algebras, unbounded operators and conditional expectations

Dosi, Anar
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.