Additive Maps Preserving Idempotency of Products or Jordan Products of Operators

Author(s):

A. Taghavi , R. Hosseinzadeh , H. Rohi

Abstract:
Let $mathcal{H}$ and $mathcal{K}$ be infinite dimensional Hilbert spaces, while $mathcal{B(H)}$ and $mathcal{B(K)}$ denote the algebras of all linear bounded operators on $mathcal{H}$ and $mathcal{K}$, respectively. We characterize the forms of additive mappings from $mathcal{B(H)}$ into $mathcal{B(K)}$ that preserve the nonzero idempotency of either Jordan products of operators or usual products of operators in both directions.
Keywords:

Operator algebra , Jordan product , Idempotent

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:11 Issue: 2, Nov 2016
Pages:
131 to 137
https://www.magiran.com/p1601383  
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