PreprintarXiv licencearXiv
Linear maps of C*-algebras preserving norm parallelism
Abstract
Two elements a,b in a normed space are parallel if |a+γb|=|a|+|b| for some |γ|=1; they form a triangle equality attaining (TEA) pair if |a+b|=|a|+|b|. For finite-dimensional complex C*-algebras other than M2(ℂ) and ℂ⊕∞ℂ, bijective linear maps on these algebras preserving parallel or TEA pairs are scalar multiples of isometries. For unital abelian algebras with spectra containing at least three points, preservation in both directions gives the same conclusion. We obtain corresponding results for type I factors, simple type I C*-algebras, and unitarily invariant operator spaces under additional continuity and finite-rank hypotheses. All results for C(X) and B(H,K) hold over both real and complex fields.
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BibTeX
@misc{li2026linear,
title = {{Linear maps of $C^*$-algebras preserving norm parallelism}},
author = {Chi-Kwong Li and Ming-Cheng Tsai and Ya-Shu Wang and Ngai-Ching Wong},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06187},
eprint = {2611.06187},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06187},
}
RIS
TY - UNPB
TI - Linear maps of C^*-algebras preserving norm parallelism
AU - Chi-Kwong Li
AU - Ming-Cheng Tsai
AU - Ya-Shu Wang
AU - Ngai-Ching Wong
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06187
UR - https://arxiv.org/abs/2611.06187
AB - Two elements a,b in a normed space are parallel if |a+γb|=|a|+|b| for some |γ|=1; they form a triangle equality attaining (TEA) pair if |a+b|=|a|+|b|. For finite-dimensional complex C^*-algebras other than M_2(ℂ) and ℂ⊕_∞ℂ, bijective linear maps on these algebras preserving parallel or TEA pairs are scalar multiples of isometries. For unital abelian algebras with spectra containing at least three points, preservation in both directions gives the same conclusion. We obtain corresponding results for type I factors, simple type I C^*-algebras, and unitarily invariant operator spaces under additional continuity and finite-rank hypotheses. All results for C(X) and B(H,K) hold over both real and complex fields.
ER -