Involutive triangular matrix algebras

In this paper we provide new examples of Banach *-subalgebras of the matrix algebra M-n (A) over a commutative unital C*-algebra 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 *-algebras and that the primitive ideals of these algebras and some of their Banach *-subalgebras are all maximal.