Minimal projections with respect to various norms

Tom 210 / 2012

Asuman Güven Aksoy, Grzegorz Lewicki Studia Mathematica 210 (2012), 1-16 MSC: Primary 41A35, 41A65; Secondary 47A12. DOI: 10.4064/sm210-1-1


A theorem of Rudin permits us to determine minimal projections not only with respect to the operator norm but with respect to various norms on operator ideals and with respect to numerical radius. We prove a general result about $N$-minimal projections where $N$ is a convex and lower semicontinuous (with respect to the strong operator topology) function and give specific examples for the cases of norms or seminorms of $p$-summing, $p$-integral and $p$-nuclear operator ideals.


  • Asuman Güven AksoyDepartment of Mathematics
    Claremont McKenna College
    Claremont, CA 91711, U.S.A.
  • Grzegorz LewickiDepartment of Mathematics and Computer Science
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland

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