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arXiv · 2109.07572

Rota-Baxter $C^{\ast}$-algebras

Zhonghua Li·Shukun Wang
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Abstract

This paper introduces the notion of Rota-Baxter $C^{\ast}$-algebras. Here a Rota-Baxter $C^{\ast}$-algebra is a $C^{\ast}$-algebra with a Rota-Baxter operator. Symmetric Rota-Baxter operators, as special cases of Rota-Baxter operators on $C^{\ast}$-algebra, are defined and studied. A theorem of Rota-Baxter operators on concrete $C^{\ast}$-algebras is given, deriving the relationship between two kinds of Rota-Baxter algebras. As a corollary, some connection between $\ast$-representations and Rota-Baxter operators is given. The notion of representations of Rota-Baxter $C^{\ast}$-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 $C^{\ast}$-algebra is reconstructed.

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Zhonghua Li, Shukun Wang. 2021-09-16. Rota-Baxter $C^{\ast}$-algebras. https://arxiv.org/abs/2109.07572

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