Regular methods of summability for direct sums of Banach spaces

摘要

Using Ramsey sets and the Galvin-Prikry partition theorem we show that the Banach-Saks property with respect to the regular positive matrix methods of summability, such as Cesaro, Norlund or Holder methods, is inherited by the countable direct sums of Banach spaces from the spaces forming this sum. (C) 2020 Elsevier Inc. All rights reserved.