Rota-Baxter $C^{\ast}$-algebras
Zhonghua Li, Shukun Wang

TL;DR
This paper develops the theory of Rota-Baxter operators within $C^{}$-algebras, exploring their properties, representations, and connections to quasidiagonal operators, thereby extending algebraic structures in functional analysis.
Contribution
It introduces Rota-Baxter $C^{}$-algebras, studies symmetric Rota-Baxter operators, and establishes their relationships with representations and quasidiagonal operators.
Findings
Established a theorem relating Rota-Baxter operators on concrete $C^{}$-algebras.
Connected $st$-representations with Rota-Baxter operators.
Reconstructed the notion of quasidiagonal operators using Rota-Baxter operators.
Abstract
This paper introduces the notion of Rota-Baxter -algebras. Here a Rota-Baxter -algebra is a -algebra with a Rota-Baxter operator. Symmetric Rota-Baxter operators, as special cases of Rota-Baxter operators on -algebra, are defined and studied. A theorem of Rota-Baxter operators on concrete -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 -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 -algebra is reconstructed.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Operator Algebra Research · Matrix Theory and Algorithms
