, Volume 29, Issue 10, pp 1871-1884
Date: 28 Mar 2013

New results on common properties of bounded linear operators RS and SR

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Abstract

Let X, Y be Banach spaces, R: X → Y and S: Y → X be bounded linear operators. When λ ≠ 0, we investigate common properties of λI − SR and λI − RS. This work should be viewed as a continuation of researches of Barnes and Lin et al.. We also apply these results obtained to B-Fredholm theory, extensions and Aluthge transforms.