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Document Details
Document Type
:
Article In Journal
Document Title
:
A simple integral representation for bounded operators in topological vector spaces
A simple integral representation for bounded operators in topological vector spaces
Subject
:
Mthematics
Document Language
:
English
Abstract
:
et E be a locally convex Hausdorff space and let E' be its topological dual, endowed with the weak* topology σ (E', E). Let S be a compact space and let us consider the space C (S,E') of all continuous functions f: S → E', equipped with the uniform topology. In this paper, we prove a simple integral representation theorem, by means of weak integrals against a scalar measure on S, for a class of linear bounded operators T: C (S,E') → E'. When E = ℑ is the Schwartz space on R{double-struck}n (thus ℑ' is the space of tempered distributions), we prove that bounded operators of this class preserve the familiar operations of distribution theory, that is, the operations of derivation and Fourier transform. Also we give an application to weak sequential convergence in this class of operators.
ISSN
:
1312885X
Journal Name
:
Applied Mathematical Sciences
Volume
:
3
Issue Number
:
17
Publishing Year
:
2009 AH
2009 AD
Number Of Pages
:
7
Article Type
:
Article
Added Date
:
Tuesday, October 6, 2009
Researchers
Researcher Name (Arabic)
Researcher Name (English)
Researcher Type
Dr Grade
Email
لخضر مبارك بلعيد مزياني
MEZIANI Lakhdar
Researcher
Doctorate
mezianilakhdar@hotmail.com
Files
File Name
Type
Description
23375.pdf
pdf
Abstract
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