Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces
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https://www.logos-verlag.de/ebooks/OA/978-3-8325-4557-4.pdfAuthor(s)
Blaimer, Bettina
Language
EnglishAbstract
It is known that a continuous linear operator T defined on a Banach function space X(μ) (over a finite measure space ( Omega,§igma,μ)) and with values in a Banach space X can be extended to a sort of optimal domain. Indeed, under certain assumptions on the space X(μ) and the operator T this optimal domain coincides with L±(mâ T), the space of all functions integrable with respect to the vector measure mâ T associated with T, and the optimal extension of T turns out to be the integration operator Iâ mâ T. In this book the idea is taken up and the corresponding theory is translated to a larger class of function spaces, namely to Fréchet function spaces X(μ) (this time over a Ï -finite measure space ( Omega,§igma,μ)). It is shown that under similar assumptions on X(μ) and T as in the case of Banach function spaces the so-called ``optimal extension process'' also works for this altered situation. In a further step the newly gained results are applied to four well-known operators defined on the Fréchet function spaces L^p-([0,1]) resp. L^p-(G) (where G is a compact Abelian group) and L^pâ textloc( mathbbR).
Keywords
Optimal domain process; Fréchet function spaces; Vector measuresDOI
10.30819/4557Webshop link
https://www.logos-verlag.de/cg ...ISBN
9783832545574Publisher
Logos Verlag BerlinPublication date and place
Berlin/Germany, 2017Imprint
Logos Verlag BerlinClassification
Calculus and mathematical analysis