Jordan and local multipliers on certain Banach algebras are multipliers

Abstract

‎In this paper‎, ‎we prove that every continuous Jordan multiplier T from a‎ C*-algebra or group algebra A into a Banach A-bimodule X is exact a multiplier‎. We also characterize a continuous linear map on C*-algebras and standard operator algebra‎s ‎through the action on zero products‎. ‎Additionally‎, ‎we show that every continuous local multiplier T from a Banach algebra A with the property $(\mathbb{B})$ into a Banach A-bimodule X is a multiplier‎. 2010 Mathematics Subject Classification. Primary 47B47, 47B49 Secondary 15A86, 46H25.