The arbitrary intersection of a family of open subsets with the -s-locally finite property is -semi-open.
Operators associated to a topology over a set and related notions.
--semi open sets and some new generalized separation axioms.
A generalization of -sets and -sets by means of operators associated with a topology and associated functions.
Browder's theorems and the spectral mapping theorem.
-generalized closed sets.
Weyl's theorem, a-Weyl's theorem and single-valued extension property.
In this paper we investigate the relation of Weyl's theorem, of a-Weyl's theorem and the single valued extension property. In particular, we establish necessary and sufficient conditions for a Banch space operator T to satisfy Weyl's theorem or a-Weyl's theorem, in the case in which T, or its dual T*, has the single valued extension property. These results improve similar results obtained by Curto and Han, Djordjevic S. V., Duggal B. P., and Y. M. Han. The theory is exemplified in the case of multipliers...
A note on preservation of spectra for two given operators
We study the relationships between the spectra derived from Fredholm theory corresponding to two given bounded linear operators acting on the same space. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from Fredholm theory and other parts of the spectra corresponding to two given operators are preserved. As an application of our results, we give conditions for which the above mentioned spectra corresponding to two multiplication operators acting on the...
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