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1997 | 38 | 1 | 227-246
Tytuł artykułu

Hilbert modules and tensor products of operator spaces

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The classical identification of the predual of B(H) (the algebra of all bounded operators on a Hilbert space H) with the projective operator space tensor product $\bar{H}\hat{⨂}H$ is extended to the context of Hilbert modules over commutative von Neumann algebras. Each bounded module homomorphism b between Hilbert modules over a general C*-algebra is shown to be completely bounded with $∥ b∥_{cb}=∥ b∥ $. The so called projective operator tensor product of two operator modules X and Y over an abelian von Neumann algebra C is introduced and if Y is a Hilbert module, this product is shown to coincide with the Haagerup tensor product of X and Y over C.
Słowa kluczowe
Rocznik
Tom
38
Numer
1
Strony
227-246
Opis fizyczny
Daty
wydano
1997
Twórcy
  • Department of Mathematics, University of Ljubljana, Ljubljana 1000, Slovenia
Bibliografia
  • [1] P. Ara and M. Mathieu, On the central Haagerup tensor product, Proc. Edinburgh Math. Soc. (2) 37 (1993), 161-174.
  • [2] D. P. Blecher, Tensor products of operator spaces II, Canad. J. Math. 44 (1992), 75-90.
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  • [6] D. P. Blecher and V. I. Paulsen, Tensor products of operator spaces, J. Funct. Anal. 99 (1991), 262-292.
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  • [9] A. Chatterjee and A. M. Sinclair, An isometry from the Haagerup tensor product into completely bounded operators, J. Operator Theory 28 (1992), 65-78.
  • [10] A. Chatterjee and R. R. Smith, The central Haagerup tensor product and maps between von Neumann algebras, J. Funct. Anal. 112 (1993), 97-120.
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  • [33] R. R. Smith, Completely bounded module maps and the Haagerup tensor product, J. Funct. Anal. 102 (1991), 156-175.
Typ dokumentu
Bibliografia
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