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Eine Erweiterung des Satzes von Schur

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Abstract

As is well-known Schur's theorem gives a necessary and sufficient condition for a conservative matrix to sum all bounded sequences. The present paper deals with two further necessary and sufficient conditions and their applications to absolutely equivalent matrices.

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Literatur

  1. BAUMANN, H.: Quotientensätze für Matrizen in der Limitierungstheorie. Math. Z. 100, 147–162 (1967)

    Google Scholar 

  2. BOOS, J.: Vergleich μ-beschränkter Wirkfelder und Singularitäten von Matrizen, Tübingen: Habilitations-schrift 1977

    Google Scholar 

  3. BOOS, J.: Konvexität der (C, α)-Verfahren. Arch. der Math. 31, 151–153 (1978)

    Google Scholar 

  4. COOKE, R. G.: Infinite Matrices and Sequence Spaces. New York: Dover Publications 1955

    Google Scholar 

  5. COOKE, R. G.: On mutual consistency and regular limits. Proc. London Math. Soc., II. s. 41, 113–125 (1936)

    Google Scholar 

  6. HARDY, G. H.: Divergent Series. Oxford: At the Clarendon Press 1949

    Google Scholar 

  7. KANGRO, G. F.: Theory of summability of sequences and series. J. Soviet Math. 5, 1–45 (1976)

    Google Scholar 

  8. MAYER, J.: Generalizations of consistency and absolute equivalence. Portugaliae Math. 24, 163–167 (1965)

    Google Scholar 

  9. MEYER-KÖNIG, W., ZELLER, K.: Zum Vergleich der Verfahren von Cesàro und Abel. Arch. der Math. 9, 191–196 (1958)

    Google Scholar 

  10. SCHUR, J.: Über lineare Transformationen in der Theorie der unendlichen Reihen. J. reine angew. Math. 151, 79–11 (1920)

    Google Scholar 

  11. ZELLER, K., BEEKMANN, W.: Theorie der Limitierungs-verfahren. 2. Aufl., Berlin-Heidelberg-New York: Springer 1970

    Google Scholar 

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Boos, J. Eine Erweiterung des Satzes von Schur. Manuscripta Math 31, 111–117 (1980). https://doi.org/10.1007/BF01303270

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  • DOI: https://doi.org/10.1007/BF01303270

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