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 optim...
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Berlin/Germany
Logos Verlag Berlin
2017
Berlin, Germany : [2017] |
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| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009439192706719 |
| Sumario: | 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). |
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| Descripción Física: | 1 online resource (137 pages) : digital file(s) Also available in print form |
| Bibliografía: | Includes bibliographical references and index. |
| ISBN: | 9783832545574 |
