Metric geometry in infinite dimensional Stiefel manifolds (Q980902)

Let \(H\) be an infinite dimensional separable Hilbert space, \(B(H)\) the space of bounded linear operators acting on \(H\) and \(\mathfrak{I}\) a separable Banach ideal of linear operators. Let \(\mathfrak{T}\) be the set of partial isometries. Fix \(v\in \mathfrak{T}\). The \(\mathfrak{T}\)-Stiefel manifold associated with \(v\) is \(St_{\mathfrak{I}}= ( v_0 \in \mathfrak{T}: v-v_0 \in \mathfrak{I}, j(v_o^*v_0,v^*v)=0)\) where \(j\) is the index of a pair of orthogonal projections. The author endows \(St_{\mathfrak{I}}\) with a Finsler metric and studies the rectifiable distance defined by it and the minimal curves with respect to this distance.