n-derivations and functional inequalities with applications

Abstract

We prove that every bounded n -derivation of a commutative factorizable Banach algebra maps into its radical.Also, the nilpotency of eigenvectors of any bounded n -derivation corresponding to its eigenvalues is derived.We introduce the notion of approximate n -derivations on a Banach algebra A and show that the separating space of an approximate n -derivation ( n > 2 ) is not necessarily an ideal, unless the Banach algebra A is factorizable.From this and some results on bounded n -derivations, we prove that every approximate n -derivation of a semisimple factorizable Banach algebra is automatically continuous and every approximate n -derivation of a commutative semisimple factorizable Banach algebra is identically zero.Some applications of our results are also provided.

Locations

• Mathematical Inequalities & Applications - View - PDF