A Variant of the Kaplansky Problem for Maps on Positive Matrices

Published 22 Apr 2022 in math.FA, math.OA, and math.RA | (2204.11622v1)

Abstract: We prove that all injective maps on positive complex matrices which preserve order and shrink spectrum are implemented by unitary or antiunitary conjugations. We show by counterexamples that all assumptions are indispensable. The result easily generalizes to maps on hermitian matrices.