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. *******************************************************************************
📌 3 Key Takeaways
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Objective & Hypothesis: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 $\mathscr{A}$.
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Key Findings & Data:For any involutive algebra, we define two involutions on the triangular matrix extensions.
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Conclusion & Impact: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. *******************************************************************************
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. *******************************************************************************
Ahmadi, M., Moussavi, A. (2020). Involutive triangular matrix algebras. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 5. https://doi.org/10.15672/hujms.559837
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