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Erschienen in:
2014 | OriginalPaper | Buchkapitel
4. Inequalities in Abstract Spaces
verfasst von : Michael J. Cloud, Byron C. Drachman, Leonid P. Lebedev
Erschienen in: Inequalities
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Abstract
Generality is gained by working in abstract spaces. For instance, all essential aspects of the topics of convergence and continuity can be studied in the context of a metric space. When we search for solutions to problems of physical interest, we must often search among the members of linear spaces (also known as vector spaces). Inequalities provide basic structure for abstract spaces like these, and we turn to a consideration of that topic in the present chapter. In doing so we present a few topics from functional analysis. Needless to say our coverage is neither broad nor deep: we hope only to catch a glimpse of inequalities in the kind of abstract setting that can unify many of our previous results before we proceed to the chapter on applications.