# Hilbert modules and tensor products of operator spaces

Banach Center Publications (1997)

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

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topMagajna, 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 -

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