Radon–Riesz property: Normed Vector Space, Limit of a Sequence, Operator Norm, Weak Topology, Banach Space, Hilbert Space, Johann Radon, Frigyes Riesz, Functional Analysis - Softcover
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Radonā€“Riesz property is a mathematical property for normed spaces that helps ensure convergence in norm. Essentially, given two assumptions (essentially weak convergence and continuity of norm), we would like to ensure convergence in the norm topology.Suppose that (X, ||Ā·||) is a normed space. We say that X has the Radonā€“Riesz property (or that X is a Radonā€“Riesz space) if whenever (xn) is a sequence in the space and x is a member of X such that (xn) converges converges weakly to x and lim_{ntoinfty} Vert x_n Vert = Vert xVert , then (xn) converges to x in norm; that is, lim_{ntoinfty} Vert x_n - xVert = 0 . Although it would appear that Johann Radon was one of the first to make significant use of the this property in 1913, M. I. Kadets and V. L. Klee also used versions of the Radonā€“Riesz property to make advancements in Banach space theory in the late 1920s. It is common for the Radonā€“Riesz property to also be referred to as the Kadetsā€“Klee property or property (H). According to Robert Megginson, the letter H does not stand for anything. It was simply referred to as property (H) in a list of properties for normed spaces that starts with (A) and ends with (H).
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- PublisherBetascript Publishing
- Publication date2010
- ISBN 10 6130343728
- ISBN 13 9786130343729
- BindingTapa blanda
- LanguageEnglish
- Number of pages80
- EditorSurhone Lambert M., Tennoe Mariam T., Henssonow Susan F.
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