Optimal Domain and Integral Extension of Operators Acting in Fréchet Function Spaces
137 Seiten, Erscheinungsjahr: 2017
Preis: 35.00 EUR
Optimal domain process, Fréchet function spaces, Vector measures
It is known that a continuous linear operator T defined on a Banach function space X(μ) (over a finite measure space (Ω,Σ,μ)) 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(μ) 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 Fr\'echet function spaces X(μ) (this time over a σ-finite measure space (Ω,Σ,μ).
It is shown that under similar assumptions on X(μ) 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 Fréchet function spaces Lp-([0,1]) resp. Lp-(G) (where G is a compact Abelian group) and Lploc .
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