Maps on $\mathcal{S}(\mathcal{H})$ preserving the difference of noninvertible algebraic operators

Authors: ZYNAB IZADI, RAHMAT SOLTANI

Abstract: The aim of this paper is to present the general structure of nonlinear surjective maps on $\mathcal S(\mathcal H)$ preserving the operator pairs in which their difference is a noninvertible algebraic operator. $\mathcal S(\mathcal H)$ represents the real Jordan algebra of bounded self-adjoint operators acting on an infinite dimensional Hilbert space $\mathcal{ H}$.

Keywords: Nonlinear preserver problem, algebraic operators, algebraic singularity

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