ON STRONGLY JORDAN ZERO-PRODUCT PRESERVING MAPS

In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a gen-eralization of Jordan zero-product preserving maps. In this di- rection, we give some illustrative examples to show that the no- tions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely di erent. 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 contin- uous.