^*-Regularity of Operator Space Projective Tensor Product of C^*-Algebras

2011/12/02 by Ajay Kumar, Kumar, Ajay, Vandana Rajpal +1
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1112.0444

arxiv created 2011/12/02 · openalex publication_date 2011/12/02 · arxiv updated 2011/12/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The Banach ^*-algebra A⊗B, the operator space projective tensor product of C^*-algebras A and B, is shown to be ^*-regular if Tomiyama's property (F) holds for A⊗_minB and A ⊗_minB=A ⊗_maxB, where ⊗_min and ⊗_max are the injective and projective C^*-cross norm, respectively. However, A⊗B has a unique C^*-norm if and only if A⊗ B has. We also discuss the property (F) of A⊗B and A⊗_hB, the Haagerup tensor product of A and B.

Citations

• Spectral synthesis for operator space projective tensor product of C^*-algebras

Related

• Arens regularity of projective tensor products
• On Banach space projective tensor product of C^*-algebras
• Geometry of C^*-algebras, the bidual of their projective tensor product, and completely bounded module maps
• Symmetry and quasi-centrality of operator space projective tensor product
• Automorphisms of Banach space projective tensor product of C*-algebras