TY - JOUR ID - 701631 TI - Maps Completely Preserving the Quadratic Operators JO - Sahand Communications in Mathematical Analysis JA - SCMA LA - en SN - 2322-5807 AU - Hosseinzadeh, Roja AD - Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P. O. Box 47416-1468, Babolsar, Iran. Y1 - 2023 PY - 2023 VL - 20 IS - 2 SP - 123 EP - 132 KW - Preserving problem KW - Completely preserving problem KW - Quadratic operator KW - Operator algebra DO - 10.22130/scma.2022.522940.901 N2 - 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. UR - https://scma.maragheh.ac.ir/article_701631.html L1 - https://scma.maragheh.ac.ir/article_701631_79f8d40ea60b10f296d7bf29833a17b5.pdf ER -