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Multiplicatively maximal numerical range-preserving maps

Published in: Quaestiones Mathematicae
Volume 48 , issue 5, pages: 783–793

DOI: 10.2989/16073606.2025.2457683

Author(s): Abdellatif BourhimSyracuse University, USA, Mohamed MabroukUmm 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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Multiplicatively maximal numerical range-preserving maps

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