Optimal domain and integral extension of operators acting in Frechet function spaces / Bettina Blaimer.

Format:

Book

Author/Creator:

Blaimer, Bettina, 1977- author.

Language:

English

Subjects (All):

Mathematics.

Physical Description:

1 online resource (137 pages) : digital file(s).

Place of Publication:

Berlin/Germany Logos Verlag Berlin 2017

Berlin, Germany : Logos Verlag Berlin GmbH, [2017]

Language Note:

In English.

System Details:

text file

Summary:

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).

Notes:

Includes bibliographical references and index.

CC BY-NC-ND

Description based on e-publication, viewed on July 13, 2021.

Other Format:

Print version:

ISBN:

9783832545574

Publisher Number:

https://doi.org/10.30819/4557