Involutive triangular matrix algebras

Authors : Morteza AHMADİ, Ahmad MOUSSAVİ

Pages : 1798-1803

Doi:10.15672/hujms.559837

View : 17 | Download : 11

Publication Date : 2020-10-06

Article Type : Research Paper

Abstract :In this paper we provide new examples of Banach $ \ast $-subalgebras of the matrix algebra $M_ninsert ignore into journalissuearticles values(\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