Maps preserving \(\eta\)-product \(A^{*}B+\eta BA^{*}\) on \(C^{*}\)-algebras. (English) Zbl 1422.47040
Let \(\mathcal A\) and \(\mathcal B\) be \(C^*\)-algebras, let \(\eta\) be a scalar different from \(0\), \(1\), and \(-1\), and let \(\Phi:\mathcal A\to \mathcal B\) be a map satisfying \(\Phi(A^*B+\eta BA^*)= \Phi(A)^*\Phi(B)+ \eta \Phi(B)\Phi(A)^*\) for all \(A,B\in \mathcal A\). The paper discusses the question under which assumptions \(\Phi\) is additive and multiplicative. The approach is based on nontrivial projections.
Reviewer: Matej Brešar (Maribor)
