The p - HH norms on Cartesian powers and sequence spaces

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Kikianty, Eder and Sinnamon, Gord (2009) The p - HH norms on Cartesian powers and sequence spaces. Journal of Mathematical Analysis and Applications, 359 (2). pp. 765-779. ISSN 0022-247X


A new family of norms is defined on the Cartesian product of n copies of a given normed space. The new norms are related to the hypergeometric means but are not restricted to the positive real numbers. Quantitative comparisons with the usual p-norms are given. The reflexivity, convexity and smoothness of the norms are shown to be closely related to the corresponding property of the underlying space. Using a limit of isometric embeddings, the norms are extended to spaces of bounded sequences that include all summable sequences. Examples are given to show that the new sequence spaces have very different properties than the usual spaces of p-summable sequences.

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Item type Article
DOI 10.1016/j.jmaa.2009.06.020
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Subjects Historical > Faculty/School/Research Centre/Department > School of Engineering and Science
Historical > FOR Classification > 0199 Other Mathematical Sciences Information Systems
Keywords ResPubID19190, Hermite–Hadamard inequality, hypergeometric mean, sequence space, Cartesian power, normed space
Citations in Scopus 5 - View on Scopus
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