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The Kadison problem on a class of commutative Banach algebras with closed cone

M. A. Toumi — 2010

Commentationes Mathematicae Universitatis Carolinae

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 $Φ$ from $A \times A$ into an arbitrary Banach space $B$ such that $Φ (a, b) = 0$ whenever $a b = 0$ , satisfies the condition $Φ (a b, c) = Φ (a, b c)$ for all $a, b, c \in A$ .

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