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A positive version of Miljutin's Theorem
Abstract
In this paper we provide a positive version of Miljutin's theorem. Namely, we show that for any uncountable compact metric spaces K and L there exists a positive isomorphism T:C(K)⟶ C(L). Moreover, the inverse of T is a regular operator, and T may be chosen so that |T|r · |T−1|r ≤ 9+6√3. The method also gives positive versions of classical nonmetrizable results for Miljutin and Dugundji compacta. In particular, if G and H are infinite compact groups of the same weight, then C(G) and C(H) are positively and regularly isomorphic with the same uniform quantitative estimate.
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BibTeX
@misc{lagunaricart2026positive,
title = {{A positive version of Miljutin's Theorem}},
author = {Javier Laguna-Ricart and Gonzalo Martínez-Cervantes and Jakub Rondoš and Alberto Salguero-Alarcón},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.14148},
eprint = {2609.14148},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14148},
}
RIS
TY - UNPB
TI - A positive version of Miljutin's Theorem
AU - Javier Laguna-Ricart
AU - Gonzalo Martínez-Cervantes
AU - Jakub Rondoš
AU - Alberto Salguero-Alarcón
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2609.14148
UR - https://arxiv.org/abs/2609.14148
AB - In this paper we provide a positive version of Miljutin's theorem. Namely, we show that for any uncountable compact metric spaces K and L there exists a positive isomorphism T:C(K)⟶ C(L). Moreover, the inverse of T is a regular operator, and T may be chosen so that |T|_r · |T^−1|_r ≤ 9+6√3. The method also gives positive versions of classical nonmetrizable results for Miljutin and Dugundji compacta. In particular, if G and H are infinite compact groups of the same weight, then C(G) and C(H) are positively and regularly isomorphic with the same uniform quantitative estimate.
ER -