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1996 | 118 | 2 | 157-168
Tytuł artykułu

Positive operator bimeasures and a noncommutative generalization

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Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
118
Numer
2
Strony
157-168
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-06-12
poprawiono
1995-11-15
Twórcy
autor
Bibliografia
  • [1] S. K. Berberian, Notes on Spectral Theory, Van Nostrand Math. Stud. 5, Van Nostrand, Princeton, N.J., 1966.
  • [2] C. Berg, J. P. R. Christensen and P. Ressel, Harmonic Analysis on Semigroups. Theory of Positive-Definite and Related Functions, Grad. Texts in Math. 100, Springer, New York, 1984.
  • [3] M. Sh. Birman, A. M. Vershik and M. Z. Solomyak, Product of commuting spectral measures need not be countably additive, Funktsional. Anal. i Prilozhen. 13 (1) (1978), 61-62; English transl.: Funct. Anal. Appl. 13 (1979), 48-49.
  • [4] P. D. Chen and J. F. Li, On the existence of product stochastic measures, Acta Math. Appl. Sinica 7 (1991), 120-134.
  • [5] E. Christensen and A. M. Sinclair, Representations of completely bounded multilinear operators, J. Funct. Anal. 72 (1987), 151-181.
  • [6] E. B. Davies, Quantum Theory of Open Systems, Academic Press, London, 1976.
  • [7] P. R. Halmos, Measure Theory, Van Nostrand, Toronto, 1950.
  • [8] A. S. Holevo, A noncommutative generalization of conditionally positive definite functions, in: Quantum Probability and Applications III (Proc. Conf. Oberwolfach, 1987), Lecture Notes in Math. 1303, Springer, Berlin, 1988, 128-148.
  • [9] S. Karni and E. Merzbach, On the extension of bimeasures, J. Anal. Math. 55 (1990), 1-16.
  • [10] C. Lance, On nuclear C*-algebras, J. Funct. Anal. 12 (1973), 157-176.
  • [11] M. Ozawa, Quantum measuring processes of continuous observables, J. Math. Phys. 25 (1984), 79-87.
  • [12] V. I. Paulsen, Completely Bounded Maps and Dilations, Pitman Res. Notes Math. 146, Longman, London, 1986.
  • [13] Z.-J. Ruan, The structure of pure completely bounded and completely positive multilinear operators, Pacific J. Math. 143 (1990), 155-173.
  • [14] W. F. Stinespring, Positive functions on C*-algebras, Proc. Amer. Math. Soc. 6 (1955), 211-216.
  • [15] M. Takesaki, Theory of Operator Algebras I, Springer, New York, 1979.
  • [16] K. Ylinen, On vector bimeasures, Ann. Mat. Pura Appl. 117 (1978), 115-138.
  • [17] K. Ylinen, Representations of bimeasures, Studia Math. 104 (1993), 269-278.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv118i2p157bwm
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