*p*-th Power Factorable Operators

Chapter

## 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 m_{T} : A → T( X_{A}). 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