The rectifiable metric on the set of closed subspaces of Hilbert space
The rectifiable metric on the set of closed subspaces of Hilbert space
Consider the set of selfadjoint projections on a fixed Hilbert space. It is well known that the connected components, under the norm topology, are the sets $\{ p:{\text {rank}}\;p = \alpha ,{\text {rank}}(1 - p) = \beta \}$, where $\alpha$ and $\beta$ are appropriate cardinal numbers. On a given component, …