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Matrix Transformations on Köthe Spaces

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Abstract

Let \(\mu \) denotes any of the classical spaces \(c_0, c\) or \(\ell _{p}\) of null, convergent or absolutely p-summable sequences and \(1\le p\le \infty \). In this paper, we characterize the classes \((\lambda (P)\,{:}\,\mu )\) of matrix transformations.

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References

  1. Allen, H.S.: Projective convergence and limit in sequence spaces. Proc. Lond. Math. Soc. 48(2), 310–338 (1945)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bennett, G.: Some inclusion theorems for sequence spaces. Pac. J. Math. 46, 17–30 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cohen, L.W., Dunford, N.: Transformations on sequence spaces. Duke Math. J. 3(4), 689–701 (1937)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cooke, R.G.: Linear Operators. Spectral Theory and Some Other Applications, Macmillan, London (1953). xii+454 pp

    MATH  Google Scholar 

  5. Deheri, G.M.: Matrix transformations on nuclear Köthe spaces. Czechoslov. Math. J 43(1), 83–93 (1993)

    MathSciNet  MATH  Google Scholar 

  6. Hahn, H.: über Folgen linearer Operationen. Monatsh. Math. Phys. 32(1), 3–88 (1922)

    Article  MathSciNet  MATH  Google Scholar 

  7. Jacob, R.T.: Matrix transformations involving simple sequence spaces. Pac. J. Math. 70(1), 179–187 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  8. Jarchow, H.: Locally Convex Spaces. B. G. Teubner, Stuttgart (1981)

    Book  MATH  Google Scholar 

  9. Kamthan, P.K., Gupta, M.: Sequence Spaces and Series Lecture Notes in Pure and Applied Mathematics, vol. 65. Marcel Dekker, New York (1981). xi+368

    Google Scholar 

  10. Knopp, K., Lorentz, G.G.: Beiträge zur absoluten Limitierung. Arch. Math. 2, 10–16 (1949)

    Article  MathSciNet  MATH  Google Scholar 

  11. Köthe, G.: Topological Vector Spaces. Springer, New York (1969)

    MATH  Google Scholar 

  12. Köthe, G., Toeplitz, O.: Lineare Räume mit unendlichen Koordinaten und Ringe unendlicher Matrizen. J. Reine Angew. Math. 171, 193–226 (1934)

    MathSciNet  MATH  Google Scholar 

  13. Terzioğlu, T.: Die diametrale Dimension von lokalkonvexen Räumen. Collect. Math. 20, 49–99 (1969)

    MathSciNet  MATH  Google Scholar 

  14. Wong, Y.C.: Schwartz Spaces, Nuclear Spaces and Tensor Products. Lecture Notes in Mathematics, vol. 726. Springer, Berlin (1979)

  15. Yeşilkayagil, M., Başar, F.: A note on some topological properties of Köthe space \(\lambda (P)\). Publ. Inst. Math. Beograd (accepted)

  16. Yeşilkayagil, M., Başar, F.: A study on certain Köthe spaces. Filomat (accepted)

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Correspondence to Medine Yeşilkayagil.

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Yeşilkayagil, M. Matrix Transformations on Köthe Spaces. Results Math 73, 29 (2018). https://doi.org/10.1007/s00025-018-0787-8

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