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p-th Power Factorable Operators

Part of the Operator Theory: Advances and Applications book series (OT, volume 180)

Abstract

Let X(μ) be a q-B.f.s. with σ-o.c. norm and E be a Banach space. A continuous linear operator T : X(μ ) → E is p-th power factorable (cf. Definition 5.1 below), for 1 ≤ p ≺ ∞, if there exists \( T_{[p]} \in \mathcal{L}(X(\mu )_{[p]} ,E) \) which coincides with T on X(μ) ⊆ X(μ)[p]. There is no a priori reason to suspect any connection between the p-th power factorability of T and its associated E-valued vector measure mT : A → T( XA). The aim of this chapter is to convince the reader that such a connection does indeed exist and has some far-reaching consequences. Henceforth, assume that T is also μ-determined.

Keywords

Banach Space Integration Operator Power Factorable Banach Lattice Vector Measure 
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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Copyright information

© Birkhäuser Verlag AG 2008

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