Optimal domain and integral extension of operators acting in Frechet function spaces / / Bettina Blaimer.
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 optim...
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Place / Publishing House: | Berlin, Germany : : Logos Verlag Berlin GmbH,, [2017] ©2017 |
Year of Publication: | 2017 |
Language: | English |
Physical Description: | 1 online resource (137 pages) :; digital file(s). |
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020 | |a 9783832545574 | ||
024 | 8 | |a https://doi.org/10.30819/4557 | |
035 | |a (CKB)4100000011479665 | ||
035 | |a (oapen)https://directory.doabooks.org/handle/20.500.12854/64485 | ||
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041 | 0 | |a eng | |
050 | 0 | 0 | |a MLCM 2024/43207 (Q) |
082 | 0 | 4 | |a 515.73 |2 22 |
100 | 1 | |a Blaimer, Bettina, |d 1977- |e author. | |
245 | 1 | 0 | |a Optimal domain and integral extension of operators acting in Frechet function spaces / |c Bettina Blaimer. |
260 | |a Berlin/Germany |b Logos Verlag Berlin |c 2017 | ||
264 | 1 | |a Berlin, Germany : |b Logos Verlag Berlin GmbH, |c [2017] | |
264 | 4 | |c ©2017 | |
300 | |a 1 online resource (137 pages) : |b digital file(s). | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |2 rda | ||
504 | |a Includes bibliographical references and index. | ||
530 | |a Also available in print form. | ||
546 | |a In English. | ||
588 | |a Description based on e-publication, viewed on July 13, 2021. | ||
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 | |f CC BY-NC-ND | ||
650 | 0 | |a Mathematics. | |
653 | |a Optimal domain process | ||
653 | |a Fréchet function spaces | ||
653 | |a Vector measures | ||
776 | 0 | 8 | |i Print version: |z 3832545573 |
ADM | |b 2024-06-14 01:14:39 Europe/Vienna |d 00 |f system |c marc21 |a 2020-10-03 22:18:00 Europe/Vienna |g false | ||
AVE | |i DOAB Directory of Open Access Books |P DOAB Directory of Open Access Books |x https://eu02.alma.exlibrisgroup.com/view/uresolver/43ACC_OEAW/openurl?u.ignore_date_coverage=true&portfolio_pid=5339671700004498&Force_direct=true |Z 5339671700004498 |b Available |8 5339671700004498 | ||
AVE | |i DOAB Directory of Open Access Books |P DOAB Directory of Open Access Books |x https://eu02.alma.exlibrisgroup.com/view/uresolver/43ACC_OEAW/openurl?u.ignore_date_coverage=true&portfolio_pid=5338836810004498&Force_direct=true |Z 5338836810004498 |b Available |8 5338836810004498 |