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On strongly Jordan zero-product preserving maps

Journal: Sahand Communications in Mathematical Analysis (Vol.3, No. 1)

Publication Date:

Authors : ;

Page : 53-61

Keywords : Strongly zero-product preserving map; Strongly Jordan zero-product preserving map; Zero-product preserving map; Jordan zero-product preserving map; Tensor product;

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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.

Last modified: 2016-03-06 17:30:56