Year: 2025
Type: article
Abstract: This paper is devoted to the space of unbounded Fredholm operators equipped with the graph topology, the subspace of operators with compact resolvents, and their subspaces consisting of self-adjoint operators. Our main results are the following: (1) Natural maps between these four spaces and classical spaces of bounded operators representing K-theory are homotopy equivalences. This provides an alternative proof of a particular case of results of Joachim. (2) The subspace of essentially positive Fredholm operators represents odd K-theory. (3) The subspace of invertible operators in each of these spaces of unbounded operators is contractible.
Source: Journal of Topology and Analysis
Author: Marina Prokhorova
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Israel Science Foundation
Awards: G11886476, G4306362543, G6613679519
OpenAlex ID: W3209667685