Pachara ChaisuriyaMahidol University2018-05-032018-05-032011-03-11Bulletin of the Malaysian Mathematical Sciences Society. Vol.34, No.1 (2011), 189-200012667052-s2.0-79952339370https://repository.li.mahidol.ac.th/handle/20.500.14594/12146In this paper, we show the relation between the Schur algebras S r Λ,Σ (β) and S r′ Λ,Σ (β); 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.Mahidol UniversityMathematicsArticleSCOPUS