{"product_id":"optimal-domain-and-integral-extension-bettina-blaimer-9783832545574","title":"Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces","description":"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\u003csup\u003e1\u003c\/sup\u003e(m\u003csub\u003eT\u003c\/sub\u003e), the space of all functions integrable with respect to the vector measure m\u003csub\u003eT\u003c\/sub\u003e associated with T, and the optimal extension of T turns out to be the integration operator I\u003csub\u003em\u003c\/sub\u003e\u003csub\u003eT\u003c\/sub\u003e. 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\u003csup\u003ep-\u003c\/sup\u003e([0,1]) resp. L\u003csup\u003ep-\u003c\/sup\u003e(G) (where G is a compact Abelian group) and L\u003csup\u003ep\u003c\/sup\u003e\u003csub\u003eloc-\u003c\/sub\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Bettina Blaimer\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3832545573\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783832545574\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Logos Verlag Berlin\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 09\/30\/2017\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 137\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.96lbs","brand":"Bettina Blaimer","offers":[{"title":"Paperback","offer_id":48450137882879,"sku":"9783832545574","price":52.5,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_f8cbe3ac-d373-4070-aa79-8360e140a1c3.jpg?v=1777266375","url":"https:\/\/www.whiterainbookhouse.com\/products\/optimal-domain-and-integral-extension-bettina-blaimer-9783832545574","provider":"WR Book House","version":"1.0","type":"link"}