Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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LINEAR MAPS PRESERVING 𝓐𝓝-OPERATORS

  • Golla, Ramesh (Department of Mathematics I. I. T. Hyderabad) ;
  • Osaka, Hiroyuki (Department of Mathematical Sciences Ritsumeikan University)
  • Received : 2019.05.16
  • Accepted : 2020.05.07
  • Published : 2020.07.31
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Abstract

Let H be a complex Hilbert space and T : H → H be a bounded linear operator. Then T is said to be norm attaining if there exists a unit vector x0 ∈ H such that ║Tx0║ = ║T║. If for any closed subspace M of H, the restriction T|M : M → H of T to M is norm attaining, then T is called an absolutely norm attaining operator or 𝓐𝓝-operator. In this note, we discuss linear maps on B(H), which preserve the class of absolutely norm attaining operators on H.

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References

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