2016/05/20 by Alex Bearden, Bearden, Clifford A.
Mathematics · Physics and Astronomy · #28A20 #46L08 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Quantum Mechanics and Applications #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1605.06521
openalex publication_date 2016/05/20 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
A Σ^*-algebra is a concrete C^*-algebra that is sequentially closed in the weak operator topology. We study an appropriate class of C^*-modules over Σ^*-algebras analogous to the class of W^*-modules (selfdual C^*-modules over W^*-algebras), and we are able to obtain Σ^*-versions of virtually all the results in the basic theory of C^*- and W^*-modules. In the second half of the paper, we study modules possessing a weak sequential form of the condition of being countably generated. A particular highlight of the paper is the "Σ^*-module completion," a Σ^*-analogue of the selfdual completion of a C^*-module over a W^*-algebra, which has an elegant uniqueness condition in the countably generated case.