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Kolmogorov Numbers for Relatively Bounded Operators |
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PP: 945-951 |
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doi:10.18576/amis/190418
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Author(s) |
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Nashat Faried,
M. A. Maher,
Asmaa Kh. Elsawy,
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Abstract |
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| In this manuscript, we extend the notion of Kolmogorov numbers of bounded linear operators to a class of unbounded operators, namely; relatively bounded operators with respect to a densely defined closed linear operator T. We get many interesting results about T-Kolmogorov numbers, for example; we show that a T-bounded operator is relatively T-compact if and only if its sequence of T -Kolmogorov numbers converges to zero. Moreover we prove that a T -bounded operator is of finite rank at most n if and only if its nth T -Kolmogorov number vanishes.
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