Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces
It 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 co...
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| Materialtyp: | Online |
| Språk: | engelska |
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Logos Verlag Berlin
2022
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| Länkar: | OCN: 1260354098 |
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| _version_ | 1869529848296243200 |
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| author | Blaimer, Bettina |
| author_browse | Blaimer, Bettina |
| author_facet | Blaimer, Bettina |
| author_sort | Blaimer, Bettina |
| collection | Directory of Open Access Books |
| description | It 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 . |
| format | Online |
| id | doab-20.500.12854ir-84276 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | Logos Verlag Berlin |
| publisherStr | Logos Verlag Berlin |
| record_format | ojs |
| spelling | doab-20.500.12854ir-842762025-07-31T01:30:25Z Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces Blaimer, Bettina Mathematics It 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 . 2022-06-19T04:04:46Z 2022-06-19T04:04:46Z 2022-06-18T05:32:57Z 2017 book OCN: 1260354098 https://library.oapen.org/handle/20.500.12657/56738 9783832545574 https://directory.doabooks.org/handle/20.500.12854/84276 eng open access image/jpeg image/jpeg image/jpeg image/jpeg image/jpeg n/a n/a n/a n/a n/a https://library.oapen.org/bitstream/20.500.12657/56738/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/56738/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/56738/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/56738/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/56738/1/external_content.pdf Logos Verlag Berlin Logos Verlag Berlin https://doi.org/10.30819/4557 https://doi.org/10.30819/4557 04b263a1-7fba-4491-9eae-1c394ac42fc3 Knowledge Unlatched 9783832545574 Knowledge Unlatched (KU) KU Open Services Logos Verlag Berlin open access |
| spellingShingle | Mathematics Blaimer, Bettina Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces |
| title | Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces |
| title_full | Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces |
| title_fullStr | Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces |
| title_full_unstemmed | Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces |
| title_short | Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces |
| title_sort | optimal domain and integral extension of operators acting in frechet function spaces |
| topic | Mathematics |
| topic_facet | Mathematics |
| url | OCN: 1260354098 |
| work_keys_str_mv | AT blaimerbettina optimaldomainandintegralextensionofoperatorsactinginfrechetfunctionspaces |