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http://dx.doi.org/10.4134/BKMS.b190494

LINEAR MAPS PRESERVING 𝓐𝓝-OPERATORS  

Golla, Ramesh (Department of Mathematics I. I. T. Hyderabad)
Osaka, Hiroyuki (Department of Mathematical Sciences Ritsumeikan University)
Publication Information
Bulletin of the Korean Mathematical Society / v.57, no.4, 2020 , pp. 831-838 More about this Journal
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.
Keywords
Compact operator; isometry; ${\mathcal{AN}}$-operator; linear preserver problem;
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