The Bishop–Phelps–Bollobás property for numerical radius in $\ell _{1}(\mathbb {C})$

Volume 218 / 2013

Antonio J. Guirao, Olena Kozhushkina Studia Mathematica 218 (2013), 41-54 MSC: 47A12, 46B28. DOI: 10.4064/sm218-1-3


We show that the set of bounded linear operators from $X$ to $X$ admits a Bishop–Phelps–Bollobás type theorem for numerical radius whenever $X$ is $\ell _1(\mathbb {C})$ or $c_0(\mathbb {C})$. As an essential tool we provide two constructive versions of the classical Bishop–Phelps–Bollobás theorem for $\ell _1(\mathbb {C})$.


  • Antonio J. GuiraoIUMPA
    Universidad Politécnica de Valencia
    46022 Valencia, Spain
  • Olena KozhushkinaDepartment of Mathematical Sciences
    Kent State University
    Kent, OH 44242, U.S.A.

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