A class of bi-contractive projections on Banach spaces

A projection \(P\) is called bi-contractive if \(\|P\|\) and \(\|I-P\|\) are both 1. In this talk we see a class of bi-contractive projections on Banach spaces, namely the Hermitian projections: \(P\) is Hermitian if the operator \(e^{itP}\) is a surjective isometry for all real \(t\). One of the main problems is to give an explicit description of Hermitian projections on different Banach spaces, well studied for many classical Banach spaces and Banach algebras. This talk presents the forms of such projections for some Banach spaces — specifically on the space \(B(X,Y)\) for Banach spaces \(X\) and \(Y\) with certain properties. Joint work with Fernanda Botelho and Dijana Ilišević.