LIFTING DERIVATIONS ANDn-WEAK AMENABILITY OF THE SECOND DUAL OF A BANACH ALGEBRA

Abstract

AbstractWe show that forn≥2,n-weak amenability of the second dual 𝒜**of a Banach algebra 𝒜 implies that of 𝒜. We also provide a positive answer for the casen=1, which sharpens some older results. Our method of proof also provides a unified approach to give short proofs for some known results in the case wheren=1.