On *-bimultipliers, Generalized *-biderivations and Related Mappings
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In this paper we define the notions of left *-bimultiplier, *-bimultiplier and generalized *-biderivation, and to prove that if a semiprime *-ring admits a left *-bimultiplier M, then M maps R × R into Z(R). In Section 3, we discuss the applications of theory of *-bimultipliers. Further, it was shown that if a semiprime *-ring R admits a symmetric generalized *-biderivation G : R × R → R with an associated nonzero symmet-ric *-biderivation B : R × R → R, then G maps R × R into Z(R). As an application, we establish corresponding results in the setting of C*-algebra.
Abstract
In this paper we define the notions of left *-bimultiplier, *-bimultiplier and generalized *-biderivation, and to prove that if a semiprime *-ring admits a left *-bimultiplier M, then M maps R × R into Z(R). In Section 3, we discuss the applications of theory of *-bimultipliers. Further, it was shown that if a semiprime *-ring R admits a symmetric generalized *-biderivation G : R × R → R with an associated nonzero symmet-ric *-biderivation B : R × R → R, then G maps R × R into Z(R). As an application, we establish corresponding results in the setting of C*-algebra.
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