Regular methods of summability and the banach-saks property for double sequences
A Banach space B is said to satisfy the Banach-Saks property with respect to a regular summability method if every bounded subsequence has a summable subsequence. We show that if a Banach space satisfies the Banach-Saks property with respect to a Robison-Hamilton regular summability method, for every bounded double sequence there exists a β-subsequence whose subsequences are all summable to the same limit.
Digital Object Identifier (DOI)
Dumitru, R., Franco, J.A., Patterson, R.F. (2021) Regular methods of summability and the banach-saks property for double sequences. Filomat, 35(5), 1489-1494. DOI: 10.2298/FIL2105489D