Some applications

  • Manuel González
  • Antonio Martínez-Abejón
Part of the Operator Theory: Advances and Applications book series (OT, volume 194)


In the previous chapters we have already described some applications of tauberian operators. For example, in Section 2.3 we can find some extensions of James’ characterization of reflexive Banach spaces and Section 2.4 shows that some properties of basic sequences can be characterized in terms of the action of the tauberian operators over them. In this chapter we present some other applications. Several of them consist of results that have been derived from the existence of a tauberian operator acting between two Banach spaces. Some others are constructions of tauberian operators that are useful in the proof of some results or provide us with counterexamples.


Banach Space Compact Subset Convex Subset Operator Ideal Compact Operator 
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Copyright information

© Birkhäuser Verlag AG 2010

Authors and Affiliations

  • Manuel González
    • 1
  • Antonio Martínez-Abejón
    • 2
  1. 1.Departamento de Matemáticas, Estadística y ComputaciónUniversidad de CantabriaSantanderSpain
  2. 2.Departamento de MatemáticasUniversidad de OviedoOviedoSpain

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