POINT DERIVATIONS ON SECOND DUALS AND UNITIZATION OF BANACH ALGEBRAS

Abstract

In this paper, among other things, we show that every point derivation on a Banach algebra A is zero if and only if every point derivation on A^♯ (the unitization of A) is zero. So we show that every point derivation on A is zero if there are no non-zero point derivations on A^{∗∗}, the second dual of A with the first Arens product.