Abstract:
A known general program, designed to endow the quotient space UA/UB of the unitary
groups UA, UB of the C∗ algebras B ⊂ A with an invariant Finsler metric, is applied to
obtain a metric for the space I(H) of partial isometries of a Hilbert space H. I(H) is a
quotient of the unitary group of B(H) × B(H), where B(H) is the algebra of bounded linear
operators in H. Under this program, the solution of a linear best approximation problem
leads to the computation of minimal geodesics in the quotient space. We find solutions of
this best approximation problem, and study properties of the minimal geodesics obtained.
