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Limit points of arithmetic means of sequences in Banach spaces

Roman Lávička (2000)

Commentationes Mathematicae Universitatis Carolinae

We shall prove the following statements: Given a sequence { a n } n = 1 in a Banach space 𝐗 enjoying the weak Banach-Saks property, there is a subsequence (or a permutation) { b n } n = 1 of the sequence { a n } n = 1 such that lim n 1 n j = 1 n b j = a whenever a belongs to the closed convex hull of the set of weak limit points of { a n } n = 1 . In case 𝐗 has the Banach-Saks property and { a n } n = 1 is bounded the converse assertion holds too. A characterization of reflexive spaces in terms of limit points and cores of bounded sequences is also given. The motivation for the...

Lower bound and upper bound of operators on block weighted sequence spaces

Rahmatollah Lashkaripour, Gholomraza Talebi (2012)

Czechoslovak Mathematical Journal

Let A = ( a n , k ) n , k 1 be a non-negative matrix. Denote by L v , p , q , F ( A ) the supremum of those L that satisfy the inequality A x v , q , F L x v , p , F , where x 0 and x l p ( v , F ) and also v = ( v n ) n = 1 is an increasing, non-negative sequence of real numbers. If p = q , we use L v , p , F ( A ) instead of L v , p , p , F ( A ) . In this paper we obtain a Hardy type formula for L v , p , q , F ( H μ ) , where H μ is a Hausdorff matrix and 0 < q p 1 . Another purpose of this paper is to establish a lower bound for A W N M v , p , F , where A W N M is the Nörlund matrix associated with the sequence W = { w n } n = 1 and 1 < p < . Our results generalize some works of Bennett, Jameson and present authors....

Multisommabilité des séries entières solutions formelles d’une équation aux q -différences linéaire analytique

Fabienne Marotte, Changgui Zhang (2000)

Annales de l'institut Fourier

Nous introduisons une version q -analogue du procédé d’accélération élémentaire d’Écalle-Martinet-Ramis et définissons la notion de série entière G q -multisommable. Nous montrons que toute série entière solution formelle d’une équation aux q -différences linéaire analytique est G q -multisommable.

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