Semi-Fredholm Theory on Hilbert C*-modules

Abstract

In this paper we establish the semi-Fredholm theory on Hilbert C*-modules as a continuation of Fredholm theory on Hilbert C*-modules established by Mishchenko and Fomenko. We give a definition of a semi-Fredholm operator on Hilbert C*-module and prove that these semi-Fredholm operators are those that are one-sided invertible modulo compact operators, that the set of proper semi-Fredholm operators is open and many other results that generalize their classical counterparts.

The paper has been accepted by the Banach Journal of Mathematical Analysis

References in corpus (2)

• The product of operators with closed range in Hilbert C*-modules
• Moore-Penrose inverse of Gram operator on Hilbert C*-modules

Cited by in corpus (7)

• Semi-Fredholm theory in C*-algebras
• On operators with closed range and semi-Fredholm operators over W*-algebras
• On upper triangular operator matrices over C*-algebras
• On Drazin invertible C*-operators and generalized C*-Weyl operators
• On compressions and generalized spectra of operators over C*-algebras
• On generalizations of semi-Fredholm operators over C*-algebras
• On New Approach to semi-Fredholm theory in unital C*-algebras