%0 Journal Article
%T Maps Completely Preserving the Quadratic Operators
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Hosseinzadeh, Roja
%D 2023
%\ 03/01/2023
%V 20
%N 2
%P 123-132
%! Maps Completely Preserving the Quadratic Operators
%K Preserving problem
%K Completely preserving problem
%K Quadratic operator
%K Operator algebra
%R 10.22130/scma.2022.522940.901
%X 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.
%U https://scma.maragheh.ac.ir/article_701631_79f8d40ea60b10f296d7bf29833a17b5.pdf