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Absolutely Summing Operator

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Dumitru Popa – One of the best experts on this subject based on the ideXlab platform.

Narcisse Randrianantoanina – One of the best experts on this subject based on the ideXlab platform.

José Rodríguez – One of the best experts on this subject based on the ideXlab platform.

  • On the equivalence of McShane and Pettis integrability in non-separable Banach spaces
    Journal of Mathematical Analysis and Applications, 2008
    Co-Authors: José Rodríguez
    Abstract:

    Abstract We show that McShane and Pettis integrability coincide for functions f : [ 0 , 1 ] → L 1 ( μ ) , where μ is any finite measure. On the other hand, assuming the Continuum Hypothesis, we prove that there exist a weakly Lindelof determined Banach space X, a scalarly null (hence Pettis integrable) function h : [ 0 , 1 ] → X and an Absolutely Summing Operator u from X to another Banach space Y such that the composition u ○ h : [ 0 , 1 ] → Y is not Bochner integrable; in particular, h is not McShane integrable.

  • Absolutely Summing Operators and integration of vector-valued functions
    Journal of Mathematical Analysis and Applications, 2006
    Co-Authors: José Rodríguez
    Abstract:

    AbstractLet (Ω,Σ,μ) be a complete probability space and u:X→Y an Absolutely Summing Operator between Banach spaces. We prove that for each Dunford integrable (i.e., scalarly integrable) function f:Ω→X the composition u○f is scalarly equivalent to a Bochner inteintegrable function. Such a composition is shown to be Bochner integrable in several cases, for instance, when f is properly measurable, Birkhoff integrable or McShane integrable, as well as when X is a subspace of an Asplund generated space or a subspace of a weakly Lindelöf space of the form C(K). We also study the continuity of the composition Operator f↦u○f. Some other applications are given

Randrianantoanina Narcisse – One of the best experts on this subject based on the ideXlab platform.

Popa Dumitru – One of the best experts on this subject based on the ideXlab platform.

  • 2-Absolutely Summing Operators on the Space C(T,X)
    Academic Press., 1999
    Co-Authors: Popa Dumitru
    Abstract:

    AbstractWe give for some Banach spaces X and Y examples of linear and continuous Operators U: C(T,X)→Y, such that U#ϕ∈As2(X,Y), for each ϕ∈C(T) and U#: C(T)→As2(X,Y) is a 2-Absolutely Summing Operator with respect to the 2-absolute norm on As2(X,Y), but U is not 2-Absolutely Summing