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arXiv · 1803.01718

Mid summable sequences: an anisotropic approach

Jamilson R. Campos·Joedson Santos
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Abstract

The notion of mid $p$-summable sequences was introduced by Karn and Sinha in 2014 and recently explored and expanded by Botelho, Campos and Santos in 2017. In this paper we design a theory of mid summable sequences in the anisotropic setting defining a new more general space called space of mid $(q,p)$-summable sequences. As a particular case of our results, we prove an inclusion relation between spaces of mid summable sequences. We also define classes of operators that deals with this new space, the mid $(q,p)$-summing operators, and prove some important results on these classes as inclusion and coincidence theorems and a Pietsch Domination-type theorem. It is worth to mentioning that these abovementioned results are new even in the particular case of the mid $p$-summable environment.

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BibTeXRIS

Jamilson R. Campos, Joedson Santos. 2018-03-05. Mid summable sequences: an anisotropic approach. https://arxiv.org/abs/1803.01718

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