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Bounded Linear Operators in Non-Archimedean Banach Spaces

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Non-Archimedean Operator Theory

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Abstract

This chapter is devoted to basic properties of bounded linear operators on non-archimedean Banach spaces. The proofs of some of these basic results will be given. Special emphasis will be upon some of these classes of bounded linear operators including finite rank linear operators, completely continuous linear operators, and Fredholm linear operators.

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References

  1. E.B. Davies, Spectral Theory and Differential Operators (Cambridge University Press, Cambridge/New York, 1995)

    Book  MATH  Google Scholar 

  2. T. Diagana, Non-archimedean Linear Operators and Applications (Nova Science Publishers, Inc., Huntington/New York, 2007)

    MATH  Google Scholar 

  3. T. Diagana, An Introduction to Classical and p-Adic Theory of Linear Operators and Applications (Nova Science Publishers, New York, 2006)

    MATH  Google Scholar 

  4. T. Diagana, R. Kerby, T.H. Miabey, F. Ramaroson, Spectral analysis for finite rank perturbations of diagonal operators in non-archimedean Hilbert space. p-Adic Numbers Ultrametric Anal. Appl. 6(3), 171—187 (2014)

    Google Scholar 

  5. B. Diarra, An operator on some ultrametric Hilbert Spaces. J. Anal. 6, 55–74 (1998)

    MathSciNet  MATH  Google Scholar 

  6. B. Diarra, Bounded linear operators on ultrametric Hilbert spaces. Afr Diaspora J. Math. 8(2), 173–181 (2009)

    MathSciNet  MATH  Google Scholar 

  7. I. Gohberg, S. Goldberg, M.A. Kaashoek, Basic Classes of Linear Operators (Basel/Boston, Birkhäuser Verlag, 1990)

    Book  MATH  Google Scholar 

  8. A.N. Kochubei, Non-Archimedean unitary operators. Methods Funct. Anal. Topol. 17(3), 219–224 (2011)

    MathSciNet  MATH  Google Scholar 

  9. A.N. Kochubei, Non-Archimedean normal operators. J. Math. Phys. 51(2), 023526, 15pp (2010)

    Google Scholar 

  10. C. Perez-Garcia, S. Vega, Perturbation theory of p-adic Fredholm and semi-Fredholm operators. Indag. Math. (N.S.) 15(1), 115–127 (2004)

    Google Scholar 

  11. C. Perez-Garcia, Semi-Fredholm operators and the Calkin algebra in p-adic analysis. I, II. Bull. Soc. Math. Belg. Sér. B 42(1), 69–101 (1990)

    Google Scholar 

  12. J.P. Serre, Completely continuous endomorphisms of p-adic Banach spaces. Publ. Math. I.H.E.S. 12, 69–85 (1962)

    Google Scholar 

  13. S. Śliwa, On Fredholm operators between non-archimedean Fréchet spaces. Compositio Mathematica 139, 113–118 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. P. Schneider, Nonarchimedean Functional Analysis (Springer, Berlin/New York, 2002)

    Book  MATH  Google Scholar 

  15. A.C.M. van Rooij, Non-archimedean Functional Analysis (Marcel Dekker Inc, New York, 1978)

    MATH  Google Scholar 

  16. M. Vishik, Non-archimedean spectral theory. J. Sov. Math. 30, 2513–2554 (1985)

    Article  MATH  Google Scholar 

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Diagana, T., Ramaroson, F. (2016). Bounded Linear Operators in Non-Archimedean Banach Spaces. In: Non-Archimedean Operator Theory. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-27323-5_3

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