Complex Manifold Structure and Algebroid of the Partially Invertible Elements Groupoid of a W*-algebra

Abstract

The goal of the present note based on [4] is a description of complex manifold structure of the groupoid $\mathcal{G}(\mathfrak{m})$ of partially invertible elements of $W^\ast\mathrm{-algebra}\;\mathfrak{m}$. We also describe Banach–Lie algebroid $\mathcal{A}(\mathfrak{m})$ of the groupoid $\mathcal{G}(\mathfrak{m})$

Mathematics Subject Classification (2010). 47C15; 58H05.