Linear maps preserving AN-operators

Golla, R. and Osaka, Hiroyuki (2020) Linear maps preserving AN-operators. Bulletin of the Korean Mathematical Society. ISSN 10158634

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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 ϵ H such that ||T x0||= ||T|| f 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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