Abstract
<p>In this paper we introduce the concept of homotopy equivalence for Hilbert $C$*-modules and investigate some properties of this equivalence relation. We then<br />present the homotopy equivalence in the context of Fredholm operators on Hilbert $C$*-modules and classify these operators in terms of their index.</p>
Highlights
One of the main ideas of algebraic topology is to consider two spaces to be equivalent if they have ’the same shape’ in a sense that is much broader than homeomorphism
In this paper we introduce the concept of homotopy equivalence for Hilbert C*-modules and investigate some properties of this equivalence relation
We present the homotopy equivalence in the context of Fredholm operators on Hilbert C*-modules and classify these operators in terms of their index
Summary
Gholamreza Abbaspour Tabadkan1 & Hessam Hosseinnezhad Department of mathematics, school of mathematics and computer science, Damghan university, Damghan, Iran. Correspondence: Hessam Hosseinnezhad, Department of mathematics, school of mathematics and computer science, Damghan university, Damghan, Iran. Received: December 23, 2015 Accepted: January 18, 2016 Online Published: January 25, 2016 doi:10.5539/jmr.v8n1p65
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