A Variant of the Kaplansky Problem for Maps on Positive Matrices
Functional Analysis
2022-04-26 v1 Operator Algebras
Rings and Algebras
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.
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Cite
@article{arxiv.2204.11622,
title = {A Variant of the Kaplansky Problem for Maps on Positive Matrices},
author = {Mateo Tomašević},
journal= {arXiv preprint arXiv:2204.11622},
year = {2022}
}
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13 pages