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Distinguished subsets and summability invariants

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References

  1. S. Banach. Théorie des opérations linéaires. Warsaw 1932.

  2. J. Copping. Inclusion theorems for conservative summation methods.Konikl. Nederl. Acad. van Wet. A 61 (1958) 485–499.

    MathSciNet  MATH  Google Scholar 

  3. H. R. Coomes and V. F. Cowling. Summability and associative infinite matrices.Mich. Math. J. 8 (1961) 65–70.

    Article  MATH  MathSciNet  Google Scholar 

  4. V. Darevsky. On Toeplitz methods,Bull. Acad. Sci. URSS., Ser. Math 11 (1947) 3–32.

    MATH  MathSciNet  Google Scholar 

  5. E. K. Dorff and A. Wilansky. Remarks on summability.J. Lond. Math. Soc. 35 (1960) 234–236.

    Article  MATH  MathSciNet  Google Scholar 

  6. W. K. Hayman and A. Wilansky, An example in summability.Bull. Amer. Math. Soc. 67 (1961) 554–555.

    Article  MATH  MathSciNet  Google Scholar 

  7. W. Jurkat, Uber Rieszsche Mittel und verwandte Klassen von Matrixtransformationen.Math. Z. 57 (1953) 353–394.

    Article  MATH  MathSciNet  Google Scholar 

  8. W. Jurkat and A. Peyerimhoff. Mittelwertsätze und Vergleichssätze für Matrixtransformationen.Math. Z. 56 (1952) 152–178.

    Article  MATH  MathSciNet  Google Scholar 

  9. G. G. Lorentz, Review of [4]Zentralblatt für Math. 34 (1950) 34.

    Google Scholar 

  10. M. S. MacPhail. On some recent developments in the theory of series.Can. J. Math. 6 (1954) 405–409.

    MATH  MathSciNet  Google Scholar 

  11. A. Peyerimhoff. Konvergenz- und Summierbarkeitsfaktoren.Math. Z. 55 (1951) 23–54.

    Article  MATH  MathSciNet  Google Scholar 

  12. D. C. Russell, Note on inclusion theorems for infinite matrices.J. Lond. Math. Soc. 33 (1958) 50–62.

    Article  MATH  Google Scholar 

  13. A. K. Snyder, On a definition for conull and coregular FK spaces.Notices Amer. Math. Soc. 10 (1963) 183.

    Google Scholar 

  14. A. Wilansky, Convergence fields of row-finite and row-infinite reversible matrices.Proc. Amer. Math. Soc. 3 (1952) 389–391.

    Article  MATH  MathSciNet  Google Scholar 

  15. A. Wilansky, Summability: The inset. The basis in summability space.Duke Math. J. 19 (1952) 647–660.

    Article  MATH  MathSciNet  Google Scholar 

  16. A. Wilansky, Functional Analysis. Blaisdell Press. 1964.

  17. A. Wilansky and K. Zeller, Summation of bounded divergent sequences, topologica methods.Trans. Amer. Math. Soc. 78 (1955) 501–509, Correction 80 (1955) 386.

    Article  MATH  MathSciNet  Google Scholar 

  18. A. Wilansky and K. Zeller, Abschnittebeschränkte Matrixtransformationen; starke Limitierbarkeit.Math. Z. 64 (1956) 258–269.

    Article  MathSciNet  Google Scholar 

  19. A. Wilansky and K. Zeller, Banach algebra and summability.Illinois. J. Math. 2 (1958) 378–385. Correction 3 (1959) 468.

    Google Scholar 

  20. A. Wilansky and K. Zeller. FH spaces and intersections of FK spaces.Mich. Math. J. 6 (1959) 349–357.

    Article  MATH  MathSciNet  Google Scholar 

  21. E. I. Yurimyae, Einige Fragen über verallgemeinerte Matrixverfahren, co-regulare und co-null Verfahren.Eesti NSV Tead. Akad. Toim. Tehn. Fuus-Mat 8 (1959) 115–121. (SeeMath. Reviews Vol. 22, No 855.)

    MathSciNet  Google Scholar 

  22. K. Zeller, Allgemeine Eigenschaften von Limitierungsverfahren.Math. Z. 53 (1951) 463–487.

    Article  MATH  MathSciNet  Google Scholar 

  23. K. Zeller, Abschnittskonvergenz in FK-Räumen.Math. Z. 53 (1951) 463–487.

    Article  MATH  MathSciNet  Google Scholar 

  24. K. Zeller, Faktorfolgen bei Limitierungsverfahren.Math. Z. 56 (1952) 134–151.

    Article  MATH  MathSciNet  Google Scholar 

  25. K. Zeller, Theorie der Limitierungsverfahren. Berlin 1958.

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Wilansky, A. Distinguished subsets and summability invariants. J. Anal. Math. 12, 327–350 (1964). https://doi.org/10.1007/BF02807439

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