On biduals of C*-tensor products

John Quigg

doi:10.1090/S0002-9939-1987-0894435-4

On biduals of C*-tensor products

John Quigg

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

Abstract

Huruya [4] has proven that, for C*-algebras A₁and A₂(A₁⊗ A₂)** = A₁**⊗ A₂** for every A₂if and only if A₁is scattered. We strengthen this by proving that (A₁⊗ A₂)** = A₁**⊗ A₂** if and only if A₁or A₂is scattered. We discuss ramifications to representation theory and related questions regarding normal representations of W*-tensor products.

Original language	English (US)
Pages (from-to)	666-668
Number of pages	3
Journal	Proceedings of the American Mathematical Society
Volume	100
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-1987-0894435-4
State	Published - Aug 1987

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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abstract = "Huruya [4] has proven that, for C*-algebras A1and A2(A1⊗ A2)** = A1**⊗ A2** for every A2if and only if A1is scattered. We strengthen this by proving that (A1⊗ A2)** = A1**⊗ A2** if and only if A1or A2is scattered. We discuss ramifications to representation theory and related questions regarding normal representations of W*-tensor products.",

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AB - Huruya [4] has proven that, for C*-algebras A1and A2(A1⊗ A2)** = A1**⊗ A2** for every A2if and only if A1is scattered. We strengthen this by proving that (A1⊗ A2)** = A1**⊗ A2** if and only if A1or A2is scattered. We discuss ramifications to representation theory and related questions regarding normal representations of W*-tensor products.

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On biduals of C*-tensor products

Abstract

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