Volume 34 • Number 1 • 2011   • A \(C^*\)-Algebra on Schur Algebras Pachara Chaisuriya Abstract. In this paper, we show the relation between the Schur algebras \(S^{r}_{\Lambda, \Sigma}(\mathcal{B})\) and \(S^{r'}_{\Lambda, \Sigma}(\mathcal{B})\), where \(1 \le r' < r < \infty \). Then we set up the involution operator in these Schur algebras and show that with this involution operator there is only one \(C^*\)-algebra among these classes of Banach algebras. Furthermore, we show the equivalence of a condition on the Schur multiplier norm and the existence of \(C^*\)-algebra. 2010 Mathematics Subject Classification: Primary 15A18; Secondary 47A10. Full text: PDF