Geodesic
Regular methods of summability and the Banach-Saks property for double sequences
Filomat, Tome 35 (2021) no. 5, p. 1489

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DOI

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.
DOI : 10.2298/FIL2105489D
Classification : 40B05, 40A05
Keywords: Banach-Saks, Double Sequences, β-subsequences 
Raluca Dumitru; Jose A Franco; Richard F Patterson. Regular methods of summability and the Banach-Saks property for double sequences. Filomat, Tome 35 (2021) no. 5, p. 1489 . doi: 10.2298/FIL2105489D
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     author = {Raluca Dumitru and Jose A Franco and Richard F Patterson},
     title = {Regular methods of summability and the {Banach-Saks} property for double sequences},
     journal = {Filomat},
     pages = {1489 },
     year = {2021},
     volume = {35},
     number = {5},
     doi = {10.2298/FIL2105489D},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2105489D/}
}
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