{"product_id":"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 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-","brand":"Logos Verlag Berlin","offers":[{"title":"Default Title","offer_id":47062762684656,"sku":"9783832545574","price":52.5,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9783832545574_p0.jpg?v=1763687834","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9783832545574","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}