Compact and weakly compact disjointness preserving operators on spaces of differentiable functions

Leung, Denny; Wang, Ya-shu

doi:10.1090/S0002-9947-2012-05831-4

Compact and weakly compact disjointness preserving operators on spaces of differentiable functions
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by Denny H. Leung and Ya-shu Wang PDF

Trans. Amer. Math. Soc. 365 (2013), 1251-1276 Request permission

Abstract:

A pair of functions defined on a set $X$ with values in a vector space $E$ is said to be disjoint if at least one of the functions takes the value $0$ at every point in $X$. An operator acting between vector-valued function spaces is disjointness preserving if it maps disjoint functions to disjoint functions. We characterize compact and weakly compact disjointness preserving operators between spaces of Banach space-valued differentiable functions.

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