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), 123128
MSC:
Primary 47B30; Secondary 47A99
MathSciNet review:
0454712
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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:
http://dx.doi.org/10.1090/S00029939197704547121
PII:
S 00029939(1977)04547121
Keywords:
Banach algebra,
maximal group,
boundary of maximal group,
bounded operator,
generalized Fredholm operator,
projection,
generalized inverse
Article copyright:
© Copyright 1977
American Mathematical Society
