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 TypeDr GradeEmail
لخضر مبارك بلعيد مزيانيMEZIANI LakhdarResearcherDoctoratemezianilakhdar@hotmail.com

Files

File NameTypeDescription
 23375.pdf pdfAbstract

Back To Researches Page