Taiwanese Journal of Mathematics

CHARACTERIZATIONS OF ALMOST CONVERGENT SEQUENCES IN A HILBERT SPACE OR IN $L^p(T)$

Chang-Pao Chen and Meng-Kuang Kuo

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Abstract

In [Acta Math. 80(1948),167-190], G. G. Lorentz characterized almost convergent sequences in $\mathbb R$ (or in $\mathbb C$) in terms of the concept of uniform convergence of the de la Vallée-Poussin means. In this paper, we give a further study on such kind of convergence for any Hilbert space or $L^p(T)$, where $1 \le p \le \infty$. Two new Cauchy forms for almost convergence are established. We prove that any of them is equivalent to the one established by Miller and Orhan. We use these forms to characterize almost convergent sequences in the aforementioned spaces in terms of coefficients.

Article information

Source
Taiwanese J. Math., Volume 11, Number 4 (2007), 1209-1219.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500404814

Digital Object Identifier
doi:10.11650/twjm/1500404814

Mathematical Reviews number (MathSciNet)
MR2348563

Zentralblatt MATH identifier
1122.40003

Subjects
Primary: 40A30: Convergence and divergence of series and sequences of functions 40G99: None of the above, but in this section 46B15: Summability and bases [See also 46A35]

Keywords
almost convergent sequences uniform convergence of de la Vallée-Poussin means Cauchy criterions Fourier coefficients Parseval formula Hausdorff-Young inequality

Citation

Chen, Chang-Pao; Kuo, Meng-Kuang. CHARACTERIZATIONS OF ALMOST CONVERGENT SEQUENCES IN A HILBERT SPACE OR IN $L^p(T)$. Taiwanese J. Math. 11 (2007), no. 4, 1209--1219. doi:10.11650/twjm/1500404814. https://projecteuclid.org/euclid.twjm/1500404814


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