Symmetric functionals on simply generated symmetric spaces
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| Titel: | Symmetric functionals on simply generated symmetric spaces |
|---|---|
| Autoren: | Levitina, Galina, Usachev, Alexandr |
| Quelle: | Journal of Mathematical Analysis and Applications. 546:129184 |
| Publication Status: | Preprint |
| Verlagsinformationen: | Elsevier BV, 2025. |
| Publikationsjahr: | 2025 |
| Schlagwörter: | singular trace, Mathematics - Functional Analysis, States of selfadjoint operator algebras, Banach limit, Connes trace formula, Mathematics - Operator Algebras, FOS: Mathematics, symmetric functional, Operator Algebras (math.OA), Noncommutative function spaces, Functional Analysis (math.FA) |
| Beschreibung: | In the present paper we suggest a construction of symmetric functionals on a large class of symmetric spaces over a semifinite von Neumann algebra. This approach establishes a bijection between the symmetric functionals on symmetric spaces and shift-invariant functionals on the space of bounded sequences. It allows to obtain a bijection between the classes of all continuous symmetric functionals on different symmetric spaces. Notably, we show that this mapping is not bijective on the class of all Dixmier traces. As an application of our results we prove an extension of the Connes trace formula for a wide class of operators and symmetric functionals. |
| Publikationsart: | Article |
| Dateibeschreibung: | application/xml |
| Sprache: | English |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2024.129184 |
| DOI: | 10.48550/arxiv.2404.13870 |
| Zugangs-URL: | http://arxiv.org/abs/2404.13870 |
| Rights: | Elsevier TDM arXiv Non-Exclusive Distribution |
| Dokumentencode: | edsair.doi.dedup.....bab31e14a7df898638a96e7fba61e887 |
| Datenbank: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstract: | In the present paper we suggest a construction of symmetric functionals on a large class of symmetric spaces over a semifinite von Neumann algebra. This approach establishes a bijection between the symmetric functionals on symmetric spaces and shift-invariant functionals on the space of bounded sequences. It allows to obtain a bijection between the classes of all continuous symmetric functionals on different symmetric spaces. Notably, we show that this mapping is not bijective on the class of all Dixmier traces. As an application of our results we prove an extension of the Connes trace formula for a wide class of operators and symmetric functionals. |
|---|---|
| ISSN: | 0022247X |
| DOI: | 10.1016/j.jmaa.2024.129184 |