Range-commutativity maps on *-algebras

Abstract: Let A and B be *-algebras, it is shown that if $\phi$ be a linear map from A into B such that $\phi(x^p)$ commutes with $\phi(x^\ast)$ for all x in A then the range of $\phi$ is commutative. The paper also studies other conditions for commutativity range of $\phi$ on *-algebra A.

Keywords: *-algebra, operator algebra, commutativity preserving map.

Classification (MSC2000): 46J10; 47B48

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