A new look at local maps on algebraic structures of matrices and operators
In a very general setting, we introduce a new type of local maps, a new sort of reflexive closure of a given class of transformations relative to a given operation that we call operational reflexive closure, and a corresponding concept of reflexivity. We calculate the operational reflexive closures...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2022
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| Sorozat: | NEW YORK JOURNAL OF MATHEMATICS
28 |
| Tárgyszavak: | |
| mtmt: | 32808481 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/37360 |
| Tartalmi kivonat: | In a very general setting, we introduce a new type of local maps, a new sort of reflexive closure of a given class of transformations relative to a given operation that we call operational reflexive closure, and a corresponding concept of reflexivity. We calculate the operational reflexive closures of some important classes of transformations and significantly strengthen former 2-reflexivity results concerning the automorphism groups of various operator structures. A typical new result is this: if phi is a map from the unitary group over a separable infinite dimensional Hilbert space into itself with the property that for any pair V, W of unitaries there is a group automorphism alpha(v,w) of the unitary group such that phi(V)phi(W) = alpha(v,w)(VW), then either phi itself or -phi is a group automorphism. This result substantially generalizes a former one on the 2-reflexivity of the automorphism group of the unitary group. We also present open problems and questions for further study. |
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| Terjedelem/Fizikai jellemzők: | 557-579 |
| ISSN: | 1076-9803 |