Relative $$\varepsilon$$ -pseudo weak demicompactness and measures of weak noncompactness
Tóm tắt
In this paper, our central focus is upon a class of linear operators acting on a Banach space X called relatively pseudo weakly demicompact operators. We clarify and determine the relationships with pseudo upper semi-Fredholm and pseudo Fredholm operators. Moreover, a characterization by means of an axiomatic measure of weak noncompactness of linear operators is established. Our results are subsequently used to investigate the relationship between the essential pseudospectrum of the sum of two linear operators and the essential pseudospectrum of each of these operators.
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