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

Sinopsis

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 I_mT. 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 L^p-([0,1]) resp. L^p-(G) (where G is a compact Abelian group) and L^p_loc-

"Sinopsis" puede pertenecer a otra edición de este libro.