Abstract
An operator idealA is said to be of Riesz type lp (0<p<∞) if any TεA(E), where E is a complex Banach space, is a Riesz operator with absolutely p-summable eigenvalues. The main purpose of this paper is to give a unified approach to the problem of estimating resolvents of operators T that belong to an arbitrary operator ideal of Riesz type lp. The method used is based on a representation of the resolvent of T2n (n>p) in the weak operator topology by characteristic determinants. The same method is used to derive estimates of Fredholm minors. The results obtained extend, generalize, and simplify results of Markus, König, and Engelbrecht and Grobler, and verify a conjecture of König. Finally, the resolvent estimates are applied to establish sufficient conditions for the completeness of principal elements.
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Reuter, F. Determinants and a unified approach to estimating resolvents of operators in operator ideals of Riesz type lp . Integr equ oper theory 8, 385–401 (1985). https://doi.org/10.1007/BF01202904
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DOI: https://doi.org/10.1007/BF01202904