^{}Department of Pure Mathematics, University of Shahrood, P. O. Box 3619995161-316, Shahrood, Iran.

Abstract

In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct product and the composition of two strongly Jordan zero-product preserving maps are again strongly Jordan zero-product preserving maps. But this fact is not the case for tensor product of them in general. Finally, we prove that every $*-$preserving linear map from a normed $*-$algebra into a $C^*-$algebra that strongly preserves Jordan zero-products is necessarily continuous.

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