- Hacettepe Journal of Mathematics and Statistics
- Vol: 49 Issue: 5
- Involutive triangular matrix algebras
Involutive triangular matrix algebras
Authors : Morteza Ahmadi, Ahmad Moussavi
Pages : 1798-1803
Doi:10.15672/hujms.559837
View : 10 | Download : 4
Publication Date : 2020-10-06
Article Type : Research
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. *******************************************************************************Keywords : primitive ideal, maximal ideal, Banach ∗-algebra, C*-algebra