Positive operator bimeasures and a noncommutative generalization

被引:0
作者
Ylinen, K [1 ]
机构
[1] UNIV CAMBRIDGE,CAMBRIDGE CB2 1TN,ENGLAND
关键词
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
For C*-algebras A and B and a Hilbert space H, a class of bilinear maps phi : A x 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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页码:157 / 168
页数:12
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共 18 条
  • [1] [Anonymous], THEORY OPERATOR ALGE
  • [2] Berberian S. K., 1966, NOTES SPECTRAL THEOR, V5
  • [3] Berg C., 1984, GRAD TEXTS MATH, V100
  • [4] BIRMAN MS, 1978, FUNKTSIONAL ANAL PRI, V13, P61
  • [5] CHEN PD, 1991, ACTA MATH APPL SINIC, V7, P120
  • [6] REPRESENTATIONS OF COMPLETELY BOUNDED MULTILINEAR OPERATORS
    CHRISTENSEN, E
    SINCLAIR, AM
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1987, 72 (01) : 151 - 181
  • [7] Davies E. B., 1976, Quantum theory of open systems
  • [8] Halmos Paul R., 1950, Measure Theory, DOI DOI 10.1007/978-1-4684-9440-2
  • [9] HOLEVO AS, 1988, LECT NOTES MATH, V1303, P128
  • [10] ON THE EXTENSION OF BIMEASURES
    KARNI, S
    MERZBACH, E
    [J]. JOURNAL D ANALYSE MATHEMATIQUE, 1990, 55 : 1 - 16