Maps Completely Preserving the Quadratic Operators

Hosseinzadeh, Roja

doi:10.22130/scma.2022.522940.901

Document Type : Research Paper

Author

Roja Hosseinzadeh

Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P. O. Box 47416-1468, Babolsar, Iran.

https://doi.org/10.22130/scma.2022.522940.901

Abstract

Let $\mathcal{A}$ and $\mathcal{B}$ be standard operator algebras on Banach spaces $\mathcal{X}$ and $\mathcal{Y}$, respectively. Let $\phi: \mathcal{A} \rightarrow \mathcal{B}$ be a bijective map. In this paper, we show that $\phi$ is completely preserving quadratic operator in both directions if and only if $\phi$ is 2-quadratic preserving operator in both directions and if and only if $\phi$ is either an isomorphism or (in the complex case) a conjugate isomorphism.

Keywords

20.1001.1.23225807.2023.20.2.6.0

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Sahand Communications in Mathematical Analysis

Maps Completely Preserving the Quadratic Operators

References

References

Volume 20, Issue 2
March 2023
Pages 123-132

Maps Completely Preserving the Quadratic Operators

References

References

Volume 20, Issue 2March 2023Pages 123-132

Volume 20, Issue 2
March 2023
Pages 123-132