Regular matrix methods of summability and real interpolation

Andrzej Kryczka, Konrad Kurlej

Abstract


We show that the Banach–Saks property with respect to a regular positive matrix method of summability is inherited by the real interpolation spaces from a space forming the interpolation family and possessing this property. The proof refers to the Galvin–Prikry theorem on Ramsey sets. The results apply to several matrix methods of summability, such as Cesaro, Nørlund or Holder methods.

Keywords


Real interpolation spaces; regular methods of summability; Banach–Saks property

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References


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DOI: http://dx.doi.org/10.17951/a.2021.75.1.53-59
Date of publication: 2021-07-24 12:07:01
Date of submission: 2021-07-21 21:45:08


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