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 ( 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 op...
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Berlin/Germany
Logos Verlag Berlin
2017
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| Online Access: | Get Fullteks DOAB: description of the publication |
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| LEADER | 02307naaaa2200289uu 4500 | ||
|---|---|---|---|
| 001 | doab_20_500_12854_64485 | ||
| 005 | 20210408 | ||
| 020 | |a 4557 | ||
| 020 | |a 9783832545574 | ||
| 024 | 7 | |a 10.30819/4557 |c doi | |
| 041 | 0 | |a English | |
| 042 | |a dc | ||
| 072 | 7 | |a PBK |2 bicssc | |
| 100 | 1 | |a Blaimer, Bettina |4 auth | |
| 245 | 1 | 0 | |a Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces |
| 260 | |a Berlin/Germany |b Logos Verlag Berlin |c 2017 | ||
| 300 | |a 1 electronic resource (137 p.) | ||
| 506 | 0 | |a Open Access |2 star |f Unrestricted online access | |
| 520 | |a 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). | ||
| 540 | |a Creative Commons |f https://creativecommons.org/licenses/by-nc-nd/4.0/ |2 cc |4 https://creativecommons.org/licenses/by-nc-nd/4.0/ | ||
| 546 | |a English | ||
| 650 | 7 | |a Calculus & mathematical analysis |2 bicssc | |
| 653 | |a Optimal domain process | ||
| 653 | |a Fréchet function spaces | ||
| 653 | |a Vector measures | ||
| 856 | 4 | 0 | |a www.oapen.org |u https://www.logos-verlag.de/ebooks/OA/978-3-8325-4557-4.pdf |7 0 |z Get Fullteks |
| 856 | 4 | 0 | |a www.oapen.org |u https://directory.doabooks.org/handle/20.500.12854/64485 |7 0 |z DOAB: description of the publication |