Crossed products by Hilbert pro-C*-bimodules versus tensor products

2014/10/28 by Maria Joiţa, Joiţa, Maria · 1 citation
Materials Science · Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Lanthanide and Transition Metal Complexes #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1410.7823

openalex publication_date 2014/10/28 · arxiv created 2015/02/15 · arxiv updated 2015/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if (X.A) and (Y,B) are two isomorphic Hilbert pro-C^∗ -bimodules, then the crossed product A×_Xℤ of A by X and the crossed product B×_Yℤ of B by Y are isomorphic as pro-C^∗-algebras. We also prove a property of "associativity" between " ⊗_min" and "×_X" as well as " ⊗_max" and "×_X". As an application of these results we show that the crossed product of a nuclear pro-C^∗ -algebra A by a full Hilbert pro-C^∗-bimodule X is a nuclear pro-C^∗-algebra.

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• Multipliers of Hilbert pro-C*-bimodules and crossed products by Hilbert pro-C*-bimodules

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