Strongly proximinal subspaces of finite codimension in $C(K)$

Tom 109 / 2007

S. Dutta, Darapaneni Narayana Colloquium Mathematicum 109 (2007), 119-128 MSC: 41A65, 46B20. DOI: 10.4064/cm109-1-10

Streszczenie

We characterize strongly proximinal subspaces of finite codimension in $C(K)$ spaces. We give two applications of our results. First, we show that the metric projection on a strongly proximinal subspace of finite codimension in $C(K)$ is Hausdorff metric continuous. Second, strong proximinality is a transitive relation for finite-codimensional subspaces of $C(K)$.

Autorzy

  • S. DuttaDepartment of Mathematics
    Ben Gurion University
    P.O.B. 653
    Beer-Sheva 84105, Israel
    and
    Stat Math Unit
    Indian Statistical Institute
    Kolkata, India
    e-mail
  • Darapaneni NarayanaDepartment of Mathematics
    Indian Institute of Science
    Bangalore 560012, India
    e-mail

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