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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
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