The rectifiable distance in the unitary Fredholm group

Abstract

Let $U_{\rm c}(\mathcal{H})=\{u: u \hbox{ unitary and } u-1 \hbox{ compact}\}$ stand for the unitary Fredholm group. We prove the following convexity result. Denote by $d_\infty$ the rectifiable distance induced by the Finsler metric given by the operato