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dc.contributor.author | PERALTA, Antonio M. | en |
dc.date.accessioned | 2023-08-31T01:00:23Z | - |
dc.date.available | 2023-08-31T01:00:23Z | - |
dc.date.issued | 2023-07 | - |
dc.identifier.uri | http://hdl.handle.net/2433/284870 | - |
dc.description.abstract | Let e and v be minimal tripotents in a JBW*-triple M. We introduce the notion of triple transition pseudo-probability from e to v as the complex number TTP(e, v) = φv(e), where φv is the unique extreme point of the closed unit ball of M∗ at which v attains its norm. In the case of two minimal projections in a von Neumann algebra, this correspond to the usual transition probability. We prove that every bijective transformation Φ preserving triple transition pseudo-probabilities between the lattices of tripotents of two atomic JBW*-triples M and N admits an extension to a bijective (complex) linear mapping between the socles of these JBW*-triples. If we additionally assume that Φ preserves orthogonality, then Φ can be extended to a surjective (complex-)linear (isometric) triple isomorphism from M onto N. In case that M and N are two spin factors or two type 1 Cartan factors we show, via techniques and results on preservers, that every bijection preserving triple transition pseudo-probabilities between the lattices of tripotents of M and N automatically preserves orthogonality, and hence admits an extension to a triple isomorphism from M onto N. | en |
dc.language.iso | eng | - |
dc.publisher | Research Institute for Mathematical Sciences, Kyoto University | en |
dc.publisher.alternative | 京都大学数理解析研究所 | ja |
dc.rights | © 2023 by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University. All rights reserved. Printed in Japan. | en |
dc.subject | 47B49 | en |
dc.subject | 46L60 | en |
dc.subject | 47N50 | en |
dc.subject | 81R15 | en |
dc.subject | 17C65 | en |
dc.subject | Wigner theorem | en |
dc.subject | minimal partial isometries | en |
dc.subject | minimal tripotents | en |
dc.subject | socle | en |
dc.subject | triple transition pseudo-probability | en |
dc.subject | preservers | en |
dc.subject | Cartan factors | en |
dc.subject | spin factors | en |
dc.subject | triple isomorphism | en |
dc.subject.ndc | 410 | - |
dc.title | Maps preserving triple transition pseudo-probabilities (Research on preserver problems on Banach algebras and related topics) | en |
dc.type | departmental bulletin paper | - |
dc.type.niitype | Departmental Bulletin Paper | - |
dc.identifier.ncid | AA12196120 | - |
dc.identifier.jtitle | 数理解析研究所講究録別冊 | ja |
dc.identifier.volume | B93 | - |
dc.identifier.spage | 1 | - |
dc.identifier.epage | 28 | - |
dc.textversion | publisher | - |
dc.sortkey | 01 | - |
dc.address | Instituto de Matemáticas de la Universidad de Granada (IMAG); Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada | es |
dcterms.accessRights | open access | - |
dc.identifier.pissn | 1881-6193 | - |
dc.identifier.jtitle-alternative | RIMS Kokyuroku Bessatsu | en |
出現コレクション: | B93 Research on preserver problems on Banach algebras and related topics |
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