A note on one-parameter groups of automorphisms
Let {αt:t∈R} and {βt:t∈R} be two commuting one-parameter groups of ∗-automorphisms of a von Neumann algebra M such that αt+α−t=βt+β−t for all t∈R. The purpose of this note is to provide a simple and short proof of the central decomposition result: αt=βt on Mp and a αt=β−t on M(1−p) for a central pro...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1990-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171290000175 |
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| _version_ | 1832559101487349760 |
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| author | A. B. Thaheem Noor Mohammad |
| author_facet | A. B. Thaheem Noor Mohammad |
| author_sort | A. B. Thaheem |
| collection | DOAJ |
| description | Let {αt:t∈R} and {βt:t∈R} be two commuting one-parameter groups of ∗-automorphisms of a von Neumann algebra M such that αt+α−t=βt+β−t for all t∈R. The purpose of this note is to provide a simple and short proof of the central decomposition result: αt=βt on Mp and a αt=β−t on M(1−p) for a central projection p∈M, without using the theory of spectral subspaces. |
| format | Article |
| id | doaj-art-d522fb0451f3497289d1ce554b7c4dc3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1990-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d522fb0451f3497289d1ce554b7c4dc32025-02-03T01:30:49ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-0113113513810.1155/S0161171290000175A note on one-parameter groups of automorphismsA. B. Thaheem0Noor Mohammad1Department of Mathematics, Quiad-i-Azam University, Islamabad, PakistanDepartment of Mathematics, Quiad-i-Azam University, Islamabad, PakistanLet {αt:t∈R} and {βt:t∈R} be two commuting one-parameter groups of ∗-automorphisms of a von Neumann algebra M such that αt+α−t=βt+β−t for all t∈R. The purpose of this note is to provide a simple and short proof of the central decomposition result: αt=βt on Mp and a αt=β−t on M(1−p) for a central projection p∈M, without using the theory of spectral subspaces.http://dx.doi.org/10.1155/S0161171290000175automorphism groupscentral projectionsinvariant projections. |
| spellingShingle | A. B. Thaheem Noor Mohammad A note on one-parameter groups of automorphisms International Journal of Mathematics and Mathematical Sciences automorphism groups central projections invariant projections. |
| title | A note on one-parameter groups of automorphisms |
| title_full | A note on one-parameter groups of automorphisms |
| title_fullStr | A note on one-parameter groups of automorphisms |
| title_full_unstemmed | A note on one-parameter groups of automorphisms |
| title_short | A note on one-parameter groups of automorphisms |
| title_sort | note on one parameter groups of automorphisms |
| topic | automorphism groups central projections invariant projections. |
| url | http://dx.doi.org/10.1155/S0161171290000175 |
| work_keys_str_mv | AT abthaheem anoteononeparametergroupsofautomorphisms AT noormohammad anoteononeparametergroupsofautomorphisms AT abthaheem noteononeparametergroupsofautomorphisms AT noormohammad noteononeparametergroupsofautomorphisms |