ON GENERALIZATIONS OF SYMMETRIC BI-DERIVATIONS ON GROUP ALGEBRAS

چکیده مقاله

In this paper, we investigate generalizations of symmetric
bi-derivations on L
∞
0 (G)
∗. For k ∈ N, we prove that if B : L
∞
0 (G)
∗ ×
L
∞
0 (G)
∗ → L
∞
0 (G)
∗ is a symmetric bi-derivation such that [B(m,m),mk] ∈
Z(L
∞
0 (G)
∗
) for all m ∈ L
∞
0 (G)
∗, then B = 0. Also, we characterize
symmetric generalized biderivations on group algebras.