Rendiconti del Circolo Matematico di Palermo

, Volume 51, Issue 1, pp 143–150 | Cite as

F + operators and classes associated with some classes of unbounded operators

  • Teresa Alvarez
Article
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Abstract

In this paper we study in a unified way the classes of all weakly compact, weakly completely continuous, unconditionally converging and Rosenthal operators in relation to a naturally associated class of operators and we generalise certain results of [9] and [10] for unbounded operators acting between normed spaces.

Keywords

Banach Space Normed Space Closed Subspace Dimensional Subspace Bounded Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Alvarez T., Cross R. W., Gouveia A. I.,Adjoint characterization of unbounded weakly compact, weakly completely continuous and unconditionally converging operators, Studia Math.,113 (1995), 283–298.MATHMathSciNetGoogle Scholar
  2. [2]
    Alvarez T., Cross R. W., Gonzalez M.,Factorization of unbounded thin and cothin operators, Quaestiones Math.,22 (1999), 519–529.MATHMathSciNetGoogle Scholar
  3. [3]
    Cross R. W.,Properties of some norm related functions of unbounded linear operators, Math. Z.,199 (1988), 285–302.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Cross R. W.,Linear transformations of Tauberian type in normal spaces, Note di Matematica,10 (1990), 193–203.MathSciNetGoogle Scholar
  5. [5]
    Cross R. W.,On a theorem of Kalton and Wilansky concerning Tauberian operators, Journal of Math. Anal. And Appl.,171 (1992), 156–170.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Cross R. W.,A characterization of almost reflexive normed spaces, Proc. Royal Irish Acad.,92 A (1992), 225–228.MathSciNetGoogle Scholar
  7. [7]
    Davies J., Figiel T, Jonhson W. B. Pelczynski A.,Factoring weakly compact operators, J. Funct. Anal.,17 (1974), 311–327.CrossRefGoogle Scholar
  8. [8]
    Goldberg S.,Unbounded linear operators, McGraw-Hill, New York, (1966).MATHGoogle Scholar
  9. [9]
    Gonzalez M., Onieva V. M.,Semi-Fredholm operators and semigroups associated with some classical operator ideals, Proc. Royal Irish Acad. Ser. A,88 A (1988), 35–38.MathSciNetGoogle Scholar
  10. [10]
    Gonzalez M., Martinez Abejon A.,Lifting unconditionally converging series and semigroups of operators, Bull. Austral. Math. Soc.,57 (1998), 135–145.MATHMathSciNetCrossRefGoogle Scholar
  11. [11]
    Howard J., Melendez K.,Characterizing operators by their first and second adjoint, Bull. Inst. Math. Acad. Sinica,5 (1977), 129–134.MATHMathSciNetGoogle Scholar
  12. [12]
    Neidinger R. D.,Properties of Tauberian operators in Banach spaces, Ph. D. Dissertation University of Texas at Austin, (1984).Google Scholar

Copyright information

© Springer 2002

Authors and Affiliations

  • Teresa Alvarez
    • 1
  1. 1.Departamento de Matematicas Facultad de CienciasUniversidad de OviedoOviedoSpain

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