Mazur spaces. (1981)

• Record Type: Journal Article
• Authors: Wilansky, Albert
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 4:Number 1(1981)
• Page Start: 39
• Page End: 53
• Publication Date: 1981
• Subjects: sequentially continuous linear maps -- classification of compact T2 spaces; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171281000021
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : A Mazur space is a locally convex topological vector spaceX such that everyf ϵ X s is continuous whereX s is the set of sequentially continuous linear functionals onX ;X s is studied whenX is of the formC ( H ), H a topological space, and whenX is the weak* dual of a locally convex space. This leads to a new classification of compactT 2 spacesH, those for which the weak* dual ofC ( H ) is a Mazur space. An open question about Banach spaces with weak* sequentially compact dual ball is settled: the dual space need not be Mazur.