Document Type : Research Paper
Author
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.
Keywords
- Strongly zero-product preserving map
- Strongly Jordan zero-product preserving map
- Zero-product preserving map
- Jordan zero-product preserving map
- Tensor product
Main Subjects