2016/07/30 by David P. Blecher, Upasana Kashyap, Blecher, David P. +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Rings, Modules, and Algebras #math.FA #math.OA
paper · pdf · doi:10.48550/arxiv.1608.00178
11 pages
openalex publication_date 2016/07/30 · arxiv created 2017/01/28 · arxiv updated 2017/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a previous paper we generalized the theory of W*-modules to the setting of modules over nonselfadjoint dual operator algebras, obtaining the class of weak*-rigged modules. At that time we promised a forthcoming paper devoted to other aspects of the theory. We fulfill this promise in the present work and its sequel "Rigged modules II", giving many new results about weak*-rigged modules and their tensor products. We also discuss the Picard group of weak* closed subalgebras of a commutative algebra. For example, we compute the weak Picard group of H∞(D), and prove that for a weak* closed function algebra A, the weak Picard group of A is a semidirect product of the automorphism group of A, and the subgroup consisting of symmetric equivalence bimodules.