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A Note on the Symmetry of Sequence Spaces

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Abstract

We give a self-contained treatment of symmetric Banach sequence spaces and some of their natural properties. We are particularly interested in the symmetry of the norm and the existence of symmetric linear functionals. Many of the presented results are known or commonly accepted, but are not found in the literature.

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References

  1. C. Bennett and R. Sharpley, Interpolation of Operators, in Pure and Applied Mathematics (Academic Press, Inc., Boston, MA, 1988), Vol. 129.

    MATH  Google Scholar 

  2. P. K. Kamthan and M. Gupta, Sequence Spaces and Series, in Lecture Notes in Pure and Applied Mathematics (Marcel Dekker, Inc., New York, 1981), Vol. 65.

    MATH  Google Scholar 

  3. S. G. Krein, Yu. I. Petunin, and E. M. Semenov, Interpolation of Linear Operators (Nauka, Moscow, 1978) [in Russian].

    Google Scholar 

  4. H. Triebel., Interpolation Theory, Function Spaces, Differential Operators (VEB Deutscher Verlag der Wissenschaften, Berlin, 1978).

    MATH  Google Scholar 

  5. D. J. H. Garling, “On symmetric sequence spaces,” Proc. London Math. Soc. 16, 85–106 (1966).

    Article  MathSciNet  Google Scholar 

  6. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I (Sequence Spaces), in Ergebnisse der Mathematik und ihrer Grenzgebiete (Springer-Verlag, Berlin-New York, 1977), Vol. 92.

    Book  Google Scholar 

  7. D. J. H. Garling, “Symmetric bases of locally convex spaces.,” Studia Math 30, 163–181 (1968).

    Article  MathSciNet  Google Scholar 

  8. F. Albiac, J. L. Ansorena, and B. Wallis, “Garling sequence spaces,” J. Lond. Math. Soc. (2) 98 (1), 204–222 (2018).

    Article  MathSciNet  Google Scholar 

  9. P. G. Dodds, B. de Pagter, E. M. Semenov, and F. A. Sukochev, “Symmetric functionals and singular traces,” Positivity 2 (1), 47–75 (1998).

    Article  MathSciNet  Google Scholar 

  10. P. G. Dodds, B. de Pagter, A. A. Sedaev, E. M. Semenov, and F. A. Sukochev., “Singular symmetric functionals and Banach limits with additional invariance properties,” Izv. Ross. Akad. Nauk Ser. Mat. 67 (6), 111–136 (2003).

    Article  MathSciNet  Google Scholar 

  11. J. B. Conway, A Course in Functional Analysis, in Graduate Texts in Mathematics (Springer-Verlag, New York, 1990), Vol. 96.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Universidad de Buenos Aires and CONICET, Buenos Aires, C1428EGA, Argentina

    D. Carando

  2. CNEA-Universidad Nacional de Cuyo and CONICET, San Carlos de Bariloche, R8402AGP, Argentina

    M. Mazzitelli

  3. Universitat Politècnica de València, València, 46022, Spain

    P. Sevilla-Peris

Authors
  1. D. Carando
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  2. M. Mazzitelli
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  3. P. Sevilla-Peris
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Correspondence to D. Carando.

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Carando, D., Mazzitelli, M. & Sevilla-Peris, P. A Note on the Symmetry of Sequence Spaces. Math Notes 110, 26–40 (2021). https://doi.org/10.1134/S0001434621070038

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  • DOI: https://doi.org/10.1134/S0001434621070038

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