Abstract
For C*-algebras A and B, the identity map from \(A \widehat{\otimes} B \) into A \(\otimes\) λ B is shown to be injective. Next, we deduce that the center of the completion of the tensor product A⊗B of two C*-algebras A and B with centers Z(A) and Z(B) under operator space projective norm is equal to \(Z(A)\widehat{\otimes}Z(B)\) . A characterization of isometric automorphisms of \(A \widehat{\otimes} B\) and A \(\otimes\) h B is also obtained.
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Dedicated to Ajit Iqbal Singh on her 65th birthday.
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Jain, R., Kumar, A. Operator space tensor products of C*-algebras. Math. Z. 260, 805–811 (2008). https://doi.org/10.1007/s00209-008-0301-1
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DOI: https://doi.org/10.1007/s00209-008-0301-1