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

Released on by Bettina Blaimer
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  • Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces Book Detail

  • Author : Bettina Blaimer
  • Release Date : 2017-09-30
  • Publisher :
  • Genre :
  • Pages : 137
  • ISBN 13 : 9783832545574
  • File Size : 69,69 MB
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Optimal Domain and Integral Extension of Operators Acting in Frechet Function Spaces by Bettina Blaimer PDF Summary

Book 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-

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Operator Theory in Function Spaces

Operator Theory in Function Spaces

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This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and