Some new characterizations of central positive elements in C⁎-algebras
In this paper, we give several characterizations for the centrality of elements in positive definite cones of C⁎-algebras. From the results to be presented, we mention only two. The first one is a characterization of centrality which is related to the usual order and to the positive part of selfadjo...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2024
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| Sorozat: | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
534 No. 2 |
| Tárgyszavak: | |
| doi: | 10.1016/j.jmaa.2023.128055 |
| mtmt: | 34516444 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/37356 |
| Tartalmi kivonat: | In this paper, we give several characterizations for the centrality of elements in positive definite cones of C⁎-algebras. From the results to be presented, we mention only two. The first one is a characterization of centrality which is related to the usual order and to the positive part of selfadjoint elements which then easily implies Sherman's famous result characterizing commutative C⁎-algebras. Furthermore, we give a substantially new type of characterization of central positive definite elements in terms of a triangle inequality. Namely, we show that for a certain generalized distance measure (emerging from the Kubo-Ando geometric mean), the triangle inequality is satisfied for a given positive definite element A and for all positive definite elements B,C of a C⁎-algebra exactly when A is central. In the proofs of the results, Kadison's transitivity theorem plays a fundamental role. © 2023 Elsevier Inc. |
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| Terjedelem/Fizikai jellemzők: | 23 |
| ISSN: | 0022-247X |