Optimal domains for kernel operators via interpolation
GP Curbera, WJ Ricker - Mathematische Nachrichten, 2002 - Wiley Online Library
GP Curbera, WJ Ricker
Mathematische Nachrichten, 2002•Wiley Online Library… Our aim here is to study this “optimal extension procedure” for particular kinds of
operators T and spaces E and X. More precisely, let E be a Banach function space on [0,1]
and X be a Banach space. We will denote by [T,X] the optimal lattice domain for T, that is,
the maximal Banach function space (containing E) to which T can be extended as a
continuous linear operator, in the sense that any other Banach function space F to which T
can be extended, is continuously embedded in [T,X]. Under certain conditions we associate …
operators T and spaces E and X. More precisely, let E be a Banach function space on [0,1]
and X be a Banach space. We will denote by [T,X] the optimal lattice domain for T, that is,
the maximal Banach function space (containing E) to which T can be extended as a
continuous linear operator, in the sense that any other Banach function space F to which T
can be extended, is continuously embedded in [T,X]. Under certain conditions we associate …
Abstract
The problem of finding optimal lattice domains for kernel operators with values in rearrangement invariant spaces on the interval [0,1] is considered. The techniques used are based on interpolation theory and integration with respect to C([0, 1])–valued measures.
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