Schur null preserving maps
Ying-Fen Lin, Donal O'Cofaigh

TL;DR
This paper characterizes Schur null preserving maps on matrix spaces, showing that surjective Schur multiplicative contractions are isometries, and extends these results to various matrix and multiplier contexts.
Contribution
It provides a comprehensive characterization of Schur null preserving maps and generalizes the result that surjective Schur multiplicative contractions are isometries.
Findings
Surjective Schur multiplicative contractions are isometries
Characterization of Schur null preserving maps on matrices
Extension of results to Schur multipliers
Abstract
We provide a characterisation of Schur multiplicative maps on both finite and infinite dimensional matrix spaces, and show that every surjective Schur multiplicative contraction is automatically an isometry. We also generalise this result and provide a characterisation of Schur null preserving maps on matrices and on Schur multipliers.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Operator Algebra Research · Holomorphic and Operator Theory
