Involutive triangular matrix algebras

Year 2020, Volume: 49 Issue: 5, 1798 - 1803, 06.10.2020

Morteza Ahmadi , Ahmad Moussavi

https://doi.org/10.15672/hujms.559837

Abstract

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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Keywords

primitive ideal , maximal ideal , Banach ∗-algebra , C*-algebra

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