PreprintCC BY 4.0arXiv
Order isomorphisms on positive cones of non-unital C*-algebras
Abstract
Let A and B be C*-algebras, not necessarily unital, and let T:A+→ B+ be a positively homogeneous order isomorphism. We first prove that T is additive and extends uniquely to a bounded real-linear order isomorphism between the self-adjoint parts of A and B. Passing to the biduals, we then obtain a representation theorem for positively homogeneous order isomorphisms. Finally, we study surjective maps between the positive cones of C*-algebras, again not necessarily unital, which preserve the norm of the arithmetic mean. This extends a previous result by removing the assumption that at least one of the algebras is unital.
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BibTeX
@misc{hatori2026order,
title = {{Order isomorphisms on positive cones of non-unital $C^*$-algebras}},
author = {Osamu Hatori and Shiho Oi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21339},
eprint = {2609.21339},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21339},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Order isomorphisms on positive cones of non-unital C^*-algebras
AU - Osamu Hatori
AU - Shiho Oi
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21339
UR - https://arxiv.org/abs/2609.21339
AB - Let A and B be C^*-algebras, not necessarily unital, and let T:A_+→ B_+ be a positively homogeneous order isomorphism. We first prove that T is additive and extends uniquely to a bounded real-linear order isomorphism between the self-adjoint parts of A and B. Passing to the biduals, we then obtain a representation theorem for positively homogeneous order isomorphisms. Finally, we study surjective maps between the positive cones of C^*-algebras, again not necessarily unital, which preserve the norm of the arithmetic mean. This extends a previous result by removing the assumption that at least one of the algebras is unital.
ER -