Bicircular projections on some Banach spaces
Let \(X\) be a complex Banach space and \(T\in{\mathfrak B}(X)\). The operator \(T\) is said to be Hermitian if \(e^{i\theta T}\) is an isometry for every \(\theta\in\mathbb{R}\). Also, a projection \(P\) on \(X\) is a bicircular projection if \(e^{i\theta} P+ e^{i\beta}(I- P)\) is an isometry for all real values of \(\alpha\) and \(\beta\). The main result of the paper is as follows. Theorem. A projection on a complex Banach space is a bicircular projection if and only if it is a Hermitian projection. Finally, some immediate consequences of this result are proved.
scientific article; zbMATH DE number 5126048