Geodesic
The Kadison problem on a class of commutative Banach algebras with closed cone
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 4, pp. 631-637 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $a,b,c\in A$.
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 $a,b,c\in A$.
Classification : 06F25, 13N05, 47B65
Keywords: derivation; local derivation 
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     author = {Toumi, M. A.},
     title = {The {Kadison} problem on a class  of commutative {Banach} algebras with closed cone},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {631--637},
     year = {2010},
     volume = {51},
     number = {4},
     mrnumber = {2858266},
     zbl = {1224.06035},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2010_51_4_a7/}
}
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Toumi, M. A. The Kadison problem on a class  of commutative Banach algebras with closed cone. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 4, pp. 631-637. http://geodesic.mathdoc.fr/item/CMUC_2010_51_4_a7/