An anisotropic approach to mid summable sequences
Volume 161 / 2020
Colloquium Mathematicum 161 (2020), 35-49
MSC: Primary 46B45; Secondary 47B10, 47L20.
DOI: 10.4064/cm7760-4-2019
Published online: 21 February 2020
Abstract
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.
