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dc.contributor.authorBlaimer, Bettina
dc.date.accessioned2022-06-18T05:32:57Z
dc.date.available2022-06-18T05:32:57Z
dc.date.issued2017
dc.identifier.urihttps://library.oapen.org/handle/20.500.12657/56738
dc.description.abstractIt is known that a continuous linear operator T defined on a Banach function space X(μ) (over a finite measure space (Ω,Σ,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 L1(mT), the space of all functions integrable with respect to the vector measure mT associated with T, and the optimal extension of T turns out to be the integration operator ImT. In this book the idea is taken up and the corresponding theory is translated to a larger class of function spaces, namely to Fr\'echet function spaces X(μ) (this time over a σ-finite measure space (Ω,Σ,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 Lp-([0,1]) resp. Lp-(G) (where G is a compact Abelian group) and Lploc .
dc.languageEnglish
dc.subject.otherMathematics
dc.titleOptimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces
dc.typebook
oapen.identifier.doihttps://doi.org/10.30819/4557
oapen.relation.isPublishedBy1059eef5-b798-421c-b07f-c6a304d3aec8
oapen.relation.isFundedByb818ba9d-2dd9-4fd7-a364-7f305aef7ee9
oapen.relation.isbn9783832545574
oapen.collectionKnowledge Unlatched (KU)
oapen.imprintLogos Verlag Berlin
oapen.identifierhttps://openresearchlibrary.org/viewer/aac952e2-0b71-4abe-a38c-723c5ed91d72
oapen.identifier.isbn9783832545574


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