Clarkson type inequalities and geometric properties of banach spaces
1999 (English)Licentiate thesis, comprehensive summary (Other academic)
In this thesis Clarkson's inequalities and their generalizations are the main tools. The technique that can be used to prove Clarkson type inequalities in more dimensions is shown. We also establish Clarkson type inequalities in general Banach spaces and point out the connections between Clarkson's inequalities and the concept of type and cotype. The classical results on the von Neumann-Jordan constant, closely related to Clarkson's inequalities, are shortly presented. The concepts of moduli of convexity and smoothness, which are connected with the geometry of Banach spaces, are discussed. Some equivalent ways of describing modulus of convexity and some properties of this function are formulated. The estimation of the modulus of convexity for L(p)-spaces is presented as well. Finally, several examples of moduli of convexity and smoothness for different spaces are described.
Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 1999. , 92 p.
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757 ; 1999:68
Research subject Mathematics; Mathematics Education
IdentifiersURN: urn:nbn:se:ltu:diva-25946Local ID: bd3825f0-d6e5-11db-8550-000ea68e967bOAI: oai:DiVA.org:ltu-25946DiVA: diva2:999104
Godkänd; 1999; 20070320 (ysko)2016-09-302016-09-30Bibliographically approved