Includes bibliographical references and index.

In English.

Description based on e-publication, viewed on July 13, 2021.

It is known that a continuous linear operator T defined on a Banach function space X(�I¼) (over a finite measure space ( Omega,§igma,�I¼)) 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(�I¼) and the operator T this optimal domain coincides with L�A�(m�a T), the space of all functions integrable with respect to the vector measure m�a T associated with T, and the optimal extension of T turns out to be the integration operator I�a m�a T. 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(�I¼) (this time over a �I -finite measure space ( Omega,§igma,�I¼)). It is shown that under similar assumptions on X(�I¼) 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 Fr�echet function spaces L^p-([0,1]) resp. L^p-(G) (where G is a compact Abelian group) and L^p�a textloc( mathbbR).

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