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

By Bettina Blaimer

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 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 Frechet 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 Frechet function spaces Lp-( 0,1]) resp. Lp-(G) (where G is a compact Abelian group) and Lploc-

• Format: Paperback
• Language: English
• ISBN: 3832545573
• ISBN13: 9783832545574
• Release Date: September 2017
• Publisher: Logos Verlag Berlin
• Length: 137 Pages
• Weight: 0.96 lbs.