Generalized Fredholm operators and the boundary of the maximal group of invertible operators

Authors:
G. W. Treese and E. P. Kelly

Journal:
Proc. Amer. Math. Soc. **67** (1977), 123-128

MSC:
Primary 47B30; Secondary 47A99

DOI:
https://doi.org/10.1090/S0002-9939-1977-0454712-1

MathSciNet review:
0454712

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *V* denote an infinite dimensional Banach space over the complex field and let denote the subset of bounded operators on *V* with the property that the null space has a closed complement and the range is closed, where the null space and range are proper subspaces of *V*. Necessary and sufficient conditions for to be in the boundary, , of the maximal group, , of invertible operators are determined. As a result, is the set of products of operators in and operators in , where is the set of projections other than the identity operator and null operator.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1977-0454712-1

Keywords:
Banach algebra,
maximal group,
boundary of maximal group,
bounded operator,
generalized Fredholm operator,
projection,
generalized inverse

Article copyright:
© Copyright 1977
American Mathematical Society