Explore
Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces
Bettina Blaimer
2017
0 Ungluers have
Faved this Work
Login to Fave
It is known that a continuous linear operator T defined on a Banach function space X(μ) (over a finite measure space (Ω,Σ,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 L1(mT), the space of all functions integrable with respect to the vector measure mT associated with T, and the optimal extension of T turns out to be the integration operator ImT. In this book the idea is taken up and the corresponding theory is translated to a larger class of function spaces, namely to Fr\'echet function spaces X(μ) (this time over a σ-finite measure space (Ω,Σ,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 Lp-([0,1]) resp. Lp-(G) (where G is a compact Abelian group) and Lploc .
This book is included in DOAB.
Why read this book? Have your say.
You must be logged in to comment.
Rights Information
Are you the author or publisher of this work? If so, you can claim it as yours by registering as an Unglue.it rights holder.Downloads
This work has been downloaded 16 times via unglue.it ebook links.
- 16 - pdf (CC BY-NC-ND) at OAPEN Library.
Keywords
- Mathematics
- Mathematics & science
Links
DOI: 10.30819/4557Editions