Loewner’s theorem for maps on operator domains
Canadian journal of mathematics, Tome 75 (2023) no. 3, pp. 912-944
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The classical Loewner’s theorem states that operator monotone functions on real intervals are described by holomorphic functions on the upper half-plane. We characterize local order isomorphisms on operator domains by biholomorphic automorphisms of the generalized upper half-plane, which is the collection of all operators with positive invertible imaginary part. We describe such maps in an explicit manner, and examine properties of maximal local order isomorphisms. Moreover, in the finite-dimensional case, we prove that every order embedding of a matrix domain is a homeomorphic order isomorphism onto another matrix domain.
Mots-clés :
Loewner’s theorem, operator domain, local order isomorphism, order embedding, biholomorphic map, generalized upper half-plane
Mori, Michiya; Šemrl, Peter. Loewner’s theorem for maps on operator domains. Canadian journal of mathematics, Tome 75 (2023) no. 3, pp. 912-944. doi: 10.4153/S0008414X22000219
@article{10_4153_S0008414X22000219,
author = {Mori, Michiya and \v{S}emrl, Peter},
title = {Loewner{\textquoteright}s theorem for maps on operator domains},
journal = {Canadian journal of mathematics},
pages = {912--944},
year = {2023},
volume = {75},
number = {3},
doi = {10.4153/S0008414X22000219},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X22000219/}
}
TY - JOUR AU - Mori, Michiya AU - Šemrl, Peter TI - Loewner’s theorem for maps on operator domains JO - Canadian journal of mathematics PY - 2023 SP - 912 EP - 944 VL - 75 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X22000219/ DO - 10.4153/S0008414X22000219 ID - 10_4153_S0008414X22000219 ER -
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