PreprintCC BY 4.0arXiv
A solution to Haagerup's problem: Normality of weights is commutatively determined
Abstract
We prove that a weight on a C*-algebra is lower semi-continuous if it is lower semi-continuous on commutative C*-subalgebras. This can be used to prove a von Neumann algebraic counterpart that a weight on a von Neumann algebra is normal if it is normal on commutative von Neumann subalgebras. This provides an affirmative solution to Haagerup's second problem (Problem 1.11) on normal weights posed in 1975.
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BibTeX
@misc{blecher2026solution,
title = {{A solution to Haagerup's problem: Normality of weights is commutatively determined}},
author = {David P. Blecher and Ikhan Choi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35774},
eprint = {2610.35774},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35774},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A solution to Haagerup's problem: Normality of weights is commutatively determined
AU - David P. Blecher
AU - Ikhan Choi
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35774
UR - https://arxiv.org/abs/2610.35774
AB - We prove that a weight on a C^*-algebra is lower semi-continuous if it is lower semi-continuous on commutative C^*-subalgebras. This can be used to prove a von Neumann algebraic counterpart that a weight on a von Neumann algebra is normal if it is normal on commutative von Neumann subalgebras. This provides an affirmative solution to Haagerup's second problem (Problem 1.11) on normal weights posed in 1975.
ER -