Arens regularity of projective tensor products

2014/01/09 by Ajay Kumar, Kumar, Ajay, Vandana Rajpal +1
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Noncommutative and Quantum Gravity Theories #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1401.1997

Abstract

For completely contractive Banach algebras A and B (respectively operator algebras A and B), the necessary and sufficient conditions for the operator space projective tensor product A\widehat⊗B (respectively the Haagerup tensor product A⊗^hB) to be Arens regular are obtained. Using the non-commutative Grothendieck's inequality, we show that, for C^*-algebras A and B, the Arens regularity of Banach algebras A⊗^hB, A\ot^γ B, A\ot^s B and A\widehat⊗B are equivalent, where ⊗^h, ⊗^γ, \ot^s and \widehat⊗ are the Haagerup, the Banach space projective tensor norm, the Schur tensor norm and the operator space projective tensor norm, respectively.

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