{ "item_title" : "Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces", "item_author" : [" Bettina Blaimer "], "item_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-", "item_img_path" : "https://covers3.booksamillion.com/covers/bam/3/83/254/557/3832545573_b.jpg", "price_data" : { "retail_price" : "53.00", "online_price" : "53.00", "our_price" : "53.00", "club_price" : "53.00", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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