Projections as averages of isometries on minimal norm ideals
In the article under review, the authors consider projections on minimal norm ideals of \(B(H)\) (the space of all bounded operators on a Hilbert space \(H\)) that are represented as the average of two surjective isometries. More precisely, they describe projections of the form \(P(T)=\frac{A_1 T B_1 + A_2 T B_2}{2}\) for all \(T \in \mathcal{I}\) (\(\mathcal{I}\) being a minimal norm ideal of \(B(H)\)), where \(A_1,A_2,B_1\) and \(B_2\) are unitary operators satisfying the commutativity conditions \(A_1 A_2=A_2 A_1\) and \(B_1 B_2=B_2 B_1\). They also characterize classes of projections of the form \(P(T)= \frac{AT + T^t B}{2}\) and \(P(T)=\frac{AT^t + T^t B}{2}\), with \(A\) and \(B\) being unitary operators satisfying certain spectral conditions, respectively.
scientific article; zbMATH DE number 5924544