Document Details

Document Type : Article In Journal 
Document Title :
Simple Integral Representation for Bounded Operators in Topological Vector Spaces
التّمثيل الصّحيح في فراغات الموجّهة الطوبولوجي
 
Subject : Simple Integral Representation for Bounded Operators in Topological Vector Spaces 
Document Language : English 
Abstract : Let E be a locally COnVeX Hausdorif space and let E’ be its topological dual, endowed with the weak* topology u (E’, E) . Let S be a. compact space and let us consider the space C (S, E’) of all continuous funct ions f: S —* E’, equipped with the uniform topology. In this paper, we irove a simple integral representation theorem, by means of weak integrals against. a sca.lar measure on S, for a class of linear bounded operators T : C (8, E’) —+ E’. When E = S is the Schwartz space on R’ (thus ‘ is the space of temp ered distributions), we prove that bounded operators of this class preserve the familiar operations of distribution theory, that is, the operations of derivat ion and Fourier transform. Also we give an application to weak sequential convergence in this class of 
ISSN : 1314-7552 
Journal Name : APPLIED MATHEMATICAL SCIENCES 
Volume : 3 
Issue Number : 18 
Publishing Year : 1430 AH
2009 AD 
Article Type : Article 
Added Date : Saturday, February 9, 2013 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
لخضر مبارك الميزانيMeziani, Lakhdar mubarkResearcherDoctoratemezianilakhdar@hotmail.com

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