A C*-Algebra on Schur Algebras

In this paper, we show the relation between the Schur algebras SΛ,Σ^r(B) and SΛ,Σ^r′(B), where 1 ≤ r r ∞: 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.