Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces - Brossura

Blaimer, Bettina

Brossura

ISBN 10: 3832545573 ISBN 13: 9783832545574

Casa editrice: Logos Verlag Berlin, 2017

Riassunto

It is known that a continuous linear operator $T$ defined on a Banach function space $X(mu)$ (over a finite measure space $(Omega,§igma,mu)$) and with values in a Banach space $X$ can be extended to a sort of optimal domain. Indeed, under certain assumptions on the space $X(mu)$ and the operator $T$ this optimal domain coincides with $L^1(m_T)$, the space of all functions integrable with respect to the vector measure $m_T$ associated with $T$, and the optimal extension of $T$ turns out to be the integration operator $I_m_T$. 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 $X(mu)$ (this time over a $sigma$-finite measure space $(Omega,§igma,mu)$). It is shown that under similar assumptions on $X(mu)$ 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 $L^p_textloc(mathbbR)$.

Dettagli dell'edizione

• Editore: Logos Verlag Berlin
• Data di pubblicazione: 2017
• Lingua: Inglese
• ISBN 10: 3832545573
• ISBN 13: 9783832545574
• Rilegatura: Copertina flessibile
• Numero di pagine: 137
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile