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Modulus Functions Sequence-Based Operator Ideal |
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PP: 65-71 |
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doi:10.18576/msl/110202
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Author(s) |
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Nashat Faried,
Mohamed Ali,
Hanan Sakr,
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Abstract |
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| The purpose of this article is to establish the ideal of bounded linear operators between arbitrary Banach spaces, for which the approximation numbers sequence is a member of the space of sequences given by a sequence of modulus functions. In addition, we developed an operator ideal utilizing certain well-known spaces such as Cesa ́ro sequence space and Orlicz sequence space as particular examples of our results. Furthermore, we showed that the operators of the finite rank are dense in the operator ideal produced by these spaces. Moreover, we verified that the operator ideal components formed by them are complete. Our results generalize those in [1] by Faried and Bakery.
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