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The set of almost convergent sequences as intersections of summability fields

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References

  1. H. T. Bell, Order summability and almost convergence. Proc. Amer. Math. Soc.38, 548–552 (1973).

    Google Scholar 

  2. D. Butković, H. Kraljević andN. Sarapa, On the almost convergence. In: Functional AnalysisII, Proc. 2nd Conf., Dubrovnik/Yugosl. 1985, LNM1242, 396–417, Berlin-Heidelberg-New York-London-Paris-Tokyo 1987.

    Google Scholar 

  3. J. P. Duran, Strongly regular matrices, almost-convergence, and Banach limits. Duke Math. J.39, 497–502 (1972).

    Google Scholar 

  4. J. D. Hill andW. T. Sledd, Summability-(Z, p) and sequences of periodic type. Canad. J. Math.16, 741–754 (1964).

    Google Scholar 

  5. W. B. Jurkat andA. Peyerimhoff, Fourier effectiveness and order summability. J. Approx. Theory4, 231–244 (1971).

    Google Scholar 

  6. G. G. Lorentz, A contribution to the theory of divergent sequences. Acta Math.80, 167–190 (1948).

    Google Scholar 

  7. F. Móricz andB. E. Rhoades, Almost convergence of double sequences and strong regularity of summability matrices. Math. Proc. Cambridge Phil. Soc.104, 283–294 (1988).

    Google Scholar 

  8. G. M. Petersen, 'Almost convergence' and uniformly distributed sequences. Quart. J. Math. Oxford Ser. (2)7, 188–191 (1956).

    Google Scholar 

  9. B. E.Rhoades, Some applications of strong regularity to Markov chains and fixed point theorems. In: Approximation TheoryIII. Proc. Conf. Hon. G. G. Lorentz, Austin/Tex. 1980, 735–740, 1980.

  10. B. E. Rhoades andX. Shi, Another way to characterize strong regularity. In: Approximation Theory and Applications. Proc. Int. Conf. 75th Birthday G. G. Lorentz, St. John's/Newfoundland, Res. Notes Math.133, 173–176, Boston-London-Melbourne 1985.

    Google Scholar 

  11. J. A. Siddiqi, Infinite matrices summing every almost periodic sequence. Pacific J. Math.39, 235–251 (1971).

    Google Scholar 

  12. K.-E. Spreng, Ordnungslimitierung, Cesàro-Verfahren und Fastkonvergenz. Analysis3, 143–158 (1983).

    Google Scholar 

  13. K.Zeller and W.Beekmann, Theorie der Limitierungsverfahren (2. Aufl.). Berlin-Heidelberg-New York 1970.

  14. A.Zygmund, Trigonometric Series, Vol. I (2nd ed.). Cambridge 1959.

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Spreng, KE. The set of almost convergent sequences as intersections of summability fields. Arch. Math 55, 366–373 (1990). https://doi.org/10.1007/BF01198475

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