2021/09/16 by Zhonghua Li, Li, Zhonghua, Shukun Wang +1
Computer Science · Mathematics · #16G99 #17B38 #46L05 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Operator Algebras (math.OA) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2109.07572
openalex publication_date 2021/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper introduces the notion of Rota-Baxter C∗-algebras. Here a Rota-Baxter C∗-algebra is a C∗-algebra with a Rota-Baxter operator. Symmetric Rota-Baxter operators, as special cases of Rota-Baxter operators on C∗-algebra, are defined and studied. A theorem of Rota-Baxter operators on concrete C∗-algebras is given, deriving the relationship between two kinds of Rota-Baxter algebras. As a corollary, some connection between ∗-representations and Rota-Baxter operators is given. The notion of representations of Rota-Baxter C∗-algebras are constructed, and a theorem of representations of direct sums of Rota-Baxter representations is derived. Finally using Rota-Baxter operators, the notion of quasidiagonal operators on C∗-algebra is reconstructed.