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 -