Properties and for Bounded Linear Operators

M. H. M. Rashid

Journal of Mathematics, 2013, vol. 2013, 1-7

Abstract:

We shall consider properties which are related to Weyl type theorem for bounded linear operators , defined on a complex Banach space . These properties, that we call property , means that the set of all poles of the resolvent of of finite rank in the usual spectrum are exactly those points of the spectrum for which is an upper semi-Fredholm with index less than or equal to 0 and we call property , means that the set of all poles of the resolvent of in the usual spectrum are exactly those points of the spectrum for which is an upper semi- -Fredholm with index less than or equal to 0. Properties and are related to a strong variants of classical Weyl’s theorem, the so-called property and property We shall characterize properties and in several ways and we shall also describe the relationships of it with the other variants of Weyl type theorems. Our main tool is localized version of the single valued extension property. Also, we consider the properties and in the frame of polaroid type operators.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:848176

DOI: 10.1155/2013/848176

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