p-th Power Factorable Operators

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


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.


Banach Space Integration Operator Power Factorable Banach Lattice Vector Measure 
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© Birkhäuser Verlag AG 2008

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