Hilbert modules and tensor products of operator spaces

Bojan Magajna

Banach Center Publications (1997)

  • Volume: 38, Issue: 1, page 227-246
  • ISSN: 0137-6934

Abstract

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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 H ¯ ⨂ ^ 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 ∥ c b = ∥ 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.

How to cite

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Magajna, Bojan. "Hilbert modules and tensor products of operator spaces." Banach Center Publications 38.1 (1997): 227-246. <http://eudml.org/doc/208632>.

@article{Magajna1997,
abstract = {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.},
author = {Magajna, Bojan},
journal = {Banach Center Publications},
keywords = {identification of the predual of ; projective operator space tensor product; Hilbert modules over commutative von Neumann algebras; bounded module homomorphism; completely bounded; projective tensor product of two operator modules; Haagerup tensor product},
language = {eng},
number = {1},
pages = {227-246},
title = {Hilbert modules and tensor products of operator spaces},
url = {http://eudml.org/doc/208632},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Magajna, Bojan
TI - Hilbert modules and tensor products of operator spaces
JO - Banach Center Publications
PY - 1997
VL - 38
IS - 1
SP - 227
EP - 246
AB - 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.
LA - eng
KW - identification of the predual of ; projective operator space tensor product; Hilbert modules over commutative von Neumann algebras; bounded module homomorphism; completely bounded; projective tensor product of two operator modules; Haagerup tensor product
UR - http://eudml.org/doc/208632
ER -

References

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