The set of partial isometries as a quotient Finsler space

ESTEBAN ANDRUCHOW

INDAGATIONES MATHEMATICAE-NEW SERIES

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2022 vol. 33 p. 736 - 752

0019-3577

A known general program, designed to endow the quotient space of the unitary groups , of the C algebras with an invariant Finsler metric, is applied to obtain a metric for the space of partial isometries of a Hilbert space . is a quotient of the unitary group of , where is the algebra of bounded linear operators in . 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.