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ArticleOriginal scientific text

Title

Positive operator bimeasures and a noncommutative generalization

Authors 1

Affiliations

  1. Department of Mathematics, University of Turku, FIN-20014 Turku, Finland

Abstract

For C*-algebras A and B and a Hilbert space H, a class of bilinear maps Φ: A× B → L(H), analogous to completely positive linear maps, is studied. A Stinespring type representation theorem is proved, and in case A and B are commutative, the class is shown to coincide with that of positive bilinear maps. As an application, the extendibility of a positive operator bimeasure to a positive operator measure is shown to be equivalent to various conditions involving positive scalar bimeasures, pairs of commuting projection-valued measures or pairs of commuting positive operator measures.

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Studia Mathematica
1996/118/2
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Pages:
157-168
Main language of publication
English
Received
1995-06-12
Accepted
1995-11-15
Published
1996
Exact and natural sciences