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ON THE EXTENDED HAAGERUP TENSOR PRODUCT IN OPERATOR SPACES

Takashi Itoh|Masaru Nagisa
대한수학회 (The Korean Mathematical Society)|2014.03|대한수학회지 (Journal of the KMS)|제51권 제2호|pp. 345-362

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키워드

operator spaceHaagerup tensor productextended Haagerup tensor productSchur product.
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초록

We describe the Haagerup tensor product ℓ∞ ⊗h ℓ ∞ and the extended Haagerup tensor product ℓ∞ ⊗h ℓ∞ in terms of Schur product maps, and show that ℓ∞ ⊗h ℓ∞∩B(ℓ2 ) (resp. ℓ∞ ⊗eh ℓ∞ ∩B(ℓ2 )) coincides with c0⊗h c0∩B(ℓ2 ) (resp. c0⊗eh c0∩B(ℓ2 )). For C*-algebras A,B, it is shown that A⊗ h B = A⊗ eh B if and only if A or B is finite-dimensional.

Abstract

We describe the Haagerup tensor product ℓ∞ ⊗h ℓ ∞ and the extended Haagerup tensor product ℓ∞ ⊗h ℓ∞ in terms of Schur product maps, and show that ℓ∞ ⊗h ℓ∞∩B(ℓ2 ) (resp. ℓ∞ ⊗eh ℓ∞ ∩B(ℓ2 )) coincides with c0⊗h c0∩B(ℓ2 ) (resp. c0⊗eh c0∩B(ℓ2 )). For C*-algebras A,B, it is shown that A⊗ h B = A⊗ eh B if and only if A or B is finite-dimensional.

참고문헌 (15)

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