# Positive operator bimeasures and a noncommutative generalization

Studia Mathematica (1996)

- Volume: 118, Issue: 2, page 157-168
- ISSN: 0039-3223

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topYlinen, Kari. "Positive operator bimeasures and a noncommutative generalization." Studia Mathematica 118.2 (1996): 157-168. <http://eudml.org/doc/216270>.

@article{Ylinen1996,

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.},

author = {Ylinen, Kari},

journal = {Studia Mathematica},

keywords = {-algebras; bilinear maps; completely positive linear maps; Stinespring type representation; positive operator bimeasure; positive operator measure; commuting projection-valued measures; pairs of commuting positive operator measures},

language = {eng},

number = {2},

pages = {157-168},

title = {Positive operator bimeasures and a noncommutative generalization},

url = {http://eudml.org/doc/216270},

volume = {118},

year = {1996},

}

TY - JOUR

AU - Ylinen, Kari

TI - Positive operator bimeasures and a noncommutative generalization

JO - Studia Mathematica

PY - 1996

VL - 118

IS - 2

SP - 157

EP - 168

AB - 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.

LA - eng

KW - -algebras; bilinear maps; completely positive linear maps; Stinespring type representation; positive operator bimeasure; positive operator measure; commuting projection-valued measures; pairs of commuting positive operator measures

UR - http://eudml.org/doc/216270

ER -

## References

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