Text

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

---

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 .

---

Availability

No copy data

Detail Information

Series Title

-

Call Number

510 BLA o

Publisher

: Logos Verlag Berlin., 2017

Collation

-

Language

English

ISBN/ISSN

9783832545574

Classification

510

Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

-

Subject(s)

Mathematics

Specific Detail Info

-

Statement of Responsibility

Bettina Blaimer

Other Information

Cataloger

Kurnadi

Source

-

Validator

maya

Digital Object Identifier (DOI)

-

Journal Volume

-

Journal Issue

-

Subtitle

-

Parallel Title

-

Other version/related

File Attachment

Comments

---

You must be logged in to post a comment