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An anisotropic approach to mid summable sequences

Volume 161 / 2020

Jamilson R. Campos, Joedson Santos 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.

Authors

  • Jamilson R. CamposDepartamento de Ciências Exatas
    Universidade Federal da Paraíba
    58.297-000 Rio Tinto, Brazil
    and
    Departamento de Matemática
    Universidade Federal da Paraíba
    58.051-900 João Pessoa, Brazil
    e-mail
    e-mail
  • Joedson SantosDepartamento de Matemática
    Universidade Federal da Paraíba
    58.051-900 João Pessoa, Brazil
    e-mail
    e-mail

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