Multiplicatively maximal numerical range-preserving maps

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Multiplicatively maximal numerical range-preserving maps

Published in: Quaestiones Mathematicae
Volume 48 , issue 5 , 2025 , pages: 783–793
DOI: 10.2989/16073606.2025.2457683
Author(s): Abdellatif Bourhim Syracuse University, USA , Mohamed Mabrouk Umm Al-Qura University, Saudi Arabia
Keywords: Primary: 47B49 , Secondary: 15A86 , 47A12 , Nonlinear preservers , numerical range , maximal numerical range , rank-one operators , finite rank operators
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Abstract

Let be the algebra of all bounded linear operators on a complex Hilbert space . For any operator , let W 0(T) be the maximal numerical range of T. We show that two maps φ 1 and φ 2 from onto itself satisfy
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