PreprintCC BY 4.0arXiv
Solutions to some open problems in matrix analysis
Abstract
We solve a problem posed by Audenaert and Kittaneh in 2012 by proving that the Aujla--Bourin subadditivity inequality can be strengthened to an optimal form. We also answer questions posed by Bourin and the second author: (1) we significantly extend both the reciprocal Lie--Trotter theorem of Audenaert and Hiai and Kato's limit theorem; (2) we determine the best constants in inequalities for sums of contractions and positive block matrices, including the sharp triangle inequality |A+B+C| ≤ 3/4 I + |A|+|B|+|C| for three contractions A,B,C; and (3) we prove a remarkable eigenvalue inequality for the symmetric modulus, thereby determining the best dimension-free lower bound in a question studied by Bourin, Lee, and Zhang.
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BibTeX
@misc{aouichaoui2026solutions,
title = {{Solutions to some open problems in matrix analysis}},
author = {Mohamed Amine Aouichaoui and Eun-Young Lee},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20094},
eprint = {2609.20094},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20094},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Solutions to some open problems in matrix analysis
AU - Mohamed Amine Aouichaoui
AU - Eun-Young Lee
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.20094
UR - https://arxiv.org/abs/2609.20094
AB - We solve a problem posed by Audenaert and Kittaneh in 2012 by proving that the Aujla--Bourin subadditivity inequality can be strengthened to an optimal form. We also answer questions posed by Bourin and the second author: (1) we significantly extend both the reciprocal Lie--Trotter theorem of Audenaert and Hiai and Kato's limit theorem; (2) we determine the best constants in inequalities for sums of contractions and positive block matrices, including the sharp triangle inequality |A+B+C| ≤ 3/4 I + |A|+|B|+|C| for three contractions A,B,C; and (3) we prove a remarkable eigenvalue inequality for the symmetric modulus, thereby determining the best dimension-free lower bound in a question studied by Bourin, Lee, and Zhang.
ER -