Constants of strong uniqueness of minimal norm-one projections

Volume 92 / 2011

A. Micek Banach Center Publications 92 (2011), 265-277 MSC: Primary 41A35, Secondary 41A44. DOI: 10.4064/bc92-0-18

Abstract

In this paper we calculate the constants of strong uniqueness of minimal norm-one projections on subspaces of codimension $k$ in the space $l^{(n)}_{\infty}$. This generalizes a main result of W. Odyniec and M. P. Prophet [J. Approx. Theory 145 (2007), 111–121]. We applied in our proof Kolmogorov's type theorem (see A. Wójcik [Approximation and Function Spaces (Gdańsk, 1979), PWN, Warszawa / North-Holland, Amsterdam, 1981, 854–866]) for strongly unique best approximation.

Authors

  • A. MicekDepartment of Mathematics
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland
    e-mail

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