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## Involutive triangular matrix algebras

In this paper we provide new examples of Banach $\ast$-subalgebras of the matrix algebra $M_n(\mathscr{A})$ over a commutative unital $C^*$-algebra $\mathscr{A}$. For any involutive algebra, we define two involutions on the triangular matrix extensions. We prove that the triangular matrix algebras over any commutative unital $C^*$-algebra are Banach ${\ast}$-algebras and that the primitive ideals of these algebras and some of their Banach $\ast$-subalgebras are all maximal.

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primitive ideal, maximal ideal, Banach ∗-algebra, C*-algebra
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Primary Language en Mathematics Mathematics Orcid: 0000-0001-9464-5245Author: Morteza AHMADİ Institution: Tarbiat Modares UniversityCountry: Iran Orcid: 0000-0002-7775-9782Author: Ahmad MOUSSAVİ (Primary Author)Institution: Tarbiat Modares UniversityCountry: Iran Publication Date : October 6, 2020