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

Blaimer, Bettina

ISBN 10: 3832545573 / ISBN 13: 9783832545574

Published by Logos Verlag Berlin, 2017

About this Item

Seller Inventory # 927831

Bibliographic Details

• Title: Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces
• Publisher: Logos Verlag Berlin
• Publication Date: 2017
• Language: English
• ISBN 10: 3832545573
• ISBN 13: 9783832545574
• Binding: paperback
• Edition: 1st.
• Condition: New
• Weight: 15 ounces

About this title

Synopsis

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(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_mT. 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 L^p-([0,1]) resp. L^p-(G) (where G is a compact Abelian group) and L^p_loc-