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may 2016 Upper-Lower and Left-Right Semi-Fredholmness
C.S. Kubrusly, B.P. Duggal
Bull. Belg. Math. Soc. Simon Stevin 23(2): 217-233 (may 2016). DOI: 10.36045/bbms/1464710115

Abstract

Upper-lower and left-right approaches coincide for semi-Fredholm operators on Hilbert spaces but, in general, they are distinct for operators on a Banach space. The purpose of this paper is to investigate the difference between the upper-lower and left-right approaches for semi-Fredholm operators on a Banach space and, in particular, to verify when these approaches coincide. The program is based on the classes $\Gamma_R[\X]$ and $\Gamma_N[\X]$ of all operators on a Banach space $\X$ with complemented range and complemented kernel. It is shown that the intersection ${\Gamma_R[\X]\cap\Gamma_N[\X]}$ is algebraically and topologically large, and also that if $\Gamma_R[\X]$ and $\Gamma_N[\X]$ are either open, or closed, or if they coincide, then there is no difference between the upper-lower and left-right approaches for semi-Fredholm operators on a Banach space.

Citation

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C.S. Kubrusly. B.P. Duggal. "Upper-Lower and Left-Right Semi-Fredholmness." Bull. Belg. Math. Soc. Simon Stevin 23 (2) 217 - 233, may 2016. https://doi.org/10.36045/bbms/1464710115

Information

Published: may 2016
First available in Project Euclid: 31 May 2016

zbMATH: 1350.47010
MathSciNet: MR3507079
Digital Object Identifier: 10.36045/bbms/1464710115

Subjects:
Primary: 47A53
Secondary: 47A10

Keywords: Complementation , essential spectrum , Fredholm operators , holes , pseudoholes

Rights: Copyright © 2016 The Belgian Mathematical Society

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Vol.23 • No. 2 • may 2016
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