Maps Completely Preserving the Quadratic Operators

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 ۲-quadratic preserving operator in both directions and if and only if \phi is either an isomorphism or (in the complex case) a conjugate isomorphism.

کلیدواژه ها:

Preserving problem ، Completely preserving problem ، Quadratic operator ، Operator algebra