M. A. Toumi
The Kadison problem on a class of commutative Banach algebras with closed cone

Comment.Math.Univ.Carolin. 51,4 (2010) 631-637.

Abstract:The main result of the paper characterizes continuous local derivations on a class of commutative Banach algebra $A$ that all of its squares are positive and satisfying the following property: Every continuous bilinear map $\Phi $ from $A\times A$ into an arbitrary Banach space $B$ such that $\Phi(a,b)=0$ whenever $ab=0$, satisfies the condition $\Phi (ab,c)=\Phi(a,bc)$ for all $a,b,c\in A$.

Keywords: derivation, local derivation
AMS Subject Classification: 06F25 13N05 47B65

PDF