Bounds For The Operator Norms Of Some Norlund Matrices

    Authors

    P. D. Johnson; R. N. Mohapatra;D. Ross

    Comments

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    Abbreviated Journal Title

    Proc. Amer. Math. Soc.

    Keywords

    Mathematics, Applied; Mathematics

    Abstract

    Suppose (p(n))(n greater than or equal to 0) is a non-increasing sequence of non-negative numbers with p(0) = 1, p(n) = Sigma(j=0)(n) P-j, n = 0, 1..., and A = A(p(n)) = (a(nk)) is the lower triangular matrix defined by a(nk) = p(n-k)/p(n), 0 less than or equal to k less than or equal to n, and a(nk) = 0, n < k. We show that the operator norm of A as a linear operator on l(p) is no greater than p/(p - 1), for 1 < p < infinity; this generalizes, yet again Hardy's inequality for sequences, and simplifies and improves, in this special case;more generally applicable results of D. Borwein, Cass, and Kratz. When the p(n) tend to a positive limit, the operator norm of A on l(p) is exactly p/(p - 1). We also give some cases when the operator norm of A on l(p) is less than p/(p - 1).

    Journal Title

    Proceedings of the American Mathematical Society

    Volume

    124

    Issue/Number

    2

    Publication Date

    1-1-1996

    Document Type

    Article

    Language

    English

    First Page

    543

    Last Page

    547

    WOS Identifier

    WOS:A1996UC15500027

    ISSN

    0002-9939

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