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.
@article{bwmeta1.element.bwnjournal-article-smv118i2p157bwm,
author = {Kari Ylinen},
title = {Positive operator bimeasures and a noncommutative generalization},
journal = {Studia Mathematica},
volume = {119},
year = {1996},
pages = {157-168},
zbl = {0862.46038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv118i2p157bwm}
}
Ylinen, Kari. Positive operator bimeasures and a noncommutative generalization. Studia Mathematica, Tome 119 (1996) pp. 157-168. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv118i2p157bwm/
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