Operators with an integral reprsentation

Cilia, Raffaella; Gutiérrez, Joaquín

doi:10.1090/proc/13249

Operators with an integral reprsentation
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by Raffaella Cilia and Joaquín M. Gutiérrez PDF

Proc. Amer. Math. Soc. 144 (2016), 5275-5290 Request permission

Corrigendum: Proc. Amer. Math. Soc. 148 (2020), 4117-4118.

Abstract:

We introduce a fairly large class of bounded linear operators between Banach spaces which admit an integral representation. It turns out that an operator belongs to this class if and only if it factors through a $C(K)$ space. As an application, we characterize Banach spaces containing no copy of $c_0$, Banach spaces containing no complemented copy of $\ell _1$, Grothendieck spaces, and $\mathscr L_{\infty }$-spaces. We also study $C(K)$-factorization and extension properties of absolutely continuous operators, giving a partial answer to a question raised in 1985 by H. Jarchow and U. Matter.

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