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

Current price: $52.50
Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces
Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces

Barnes and Noble

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

Current price: $52.50

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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 Im T. 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-

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