Banach Lie groupoid of partial isometries over restricted Grassmannian

TL;DR

This paper constructs a Banach Lie groupoid structure on the set of partial isometries over the restricted Grassmannian, advancing the understanding of their differential geometric properties within operator algebras.

Contribution

It introduces a differential structure on partial isometries over the restricted Grassmannian, establishing a Banach Lie groupoid framework.

Findings

Partial isometries form a Banach Lie groupoid

Differential structure is constructed on these partial isometries

Enhances geometric understanding of operator algebra structures

Abstract

The set of partial isometries in a W*-algebra possesses a structure of Banach Lie groupoid. In this paper the differential structure on the set of partial isometries over the restricted Grassmannian is constructed, which makes it into a Banach Lie groupoid.