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An anisotropic approach to mid summable sequences. (English) Zbl 07262525
Summary: The purpose of this paper is to present an anisotropic theory for mid summable sequences by defining a more general space, called the 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 a class of operators acting on this new space, the mid $$(q,p)$$-summing operators, and prove some inclusion and coincidence results and a Pietsch domination-type theorem. It is worth mentioning that the above results are new even in the particular case of mid $$p$$-summable sequences.
##### MSC:
 46B45 Banach sequence spaces 47B10 Linear operators belonging to operator ideals (nuclear, $$p$$-summing, in the Schatten-von Neumann classes, etc.) 47L20 Operator ideals
##### Keywords:
Banach sequence spaces; operator ideals; summing operators
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##### References:
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