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# On Biduals of C*-Tensor Products

John C. Quigg
Proceedings of the American Mathematical Society
Vol. 100, No. 4 (Aug., 1987), pp. 666-668
DOI: 10.2307/2046703
Stable URL: http://www.jstor.org/stable/2046703
Page Count: 3
Huruya [4] has proven that, for C*-algebras A1 and A2, $(A_1 \otimes A_2)^{\ast\ast} = A^{\ast\ast}_1 \overline\otimes A^{\ast\ast}_2$ for every A2 if and only if A1 is scattered. We strengthen this by proving that $(A_1 \otimes A_2)^{\ast\ast} = A^{\ast\ast}_1 \overline\otimes A^{\ast\ast}_2$ if and only if A1 or A2 is scattered. We discuss ramifications to representation theory and related questions regarding normal representations of W*-tensor products.