On the operator equation α+α−1=β+β−1
Let α,β be ∗-automorphisms of a von Neumann algebra M satisfying the operator equation α+α−1=β+β−1. In this paper we use new techniques (which are useful in noncommutative situations as well) to provide alternate proofs of the results:- If α,β commute then there is a central projection p in M such t...
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| Format: | Article |
| Language: | English |
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Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171286000923 |
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| _version_ | 1832545623748902912 |
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| author | A. B. Thaheem |
| author_facet | A. B. Thaheem |
| author_sort | A. B. Thaheem |
| collection | DOAJ |
| description | Let α,β be ∗-automorphisms of a von Neumann algebra M satisfying the operator equation α+α−1=β+β−1. In this paper we use new techniques (which are useful in noncommutative situations as well) to provide alternate proofs of the results:- If α,β commute then there is a central projection p in M such that α=β on MP and α=β−1 on M(1−P); If M=B(H), the algebra of all bounded operators on a Hilbert space H, then α=β or α=β−1. |
| format | Article |
| id | doaj-art-0bdc3f5af68c45388ae06d33fe2fe6f9 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1986-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0bdc3f5af68c45388ae06d33fe2fe6f92025-02-03T07:25:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019476777010.1155/S0161171286000923On the operator equation α+α−1=β+β−1A. B. Thaheem0Department of Mathematics, Quaid-i-Azam University, Islamabad, PakistanLet α,β be ∗-automorphisms of a von Neumann algebra M satisfying the operator equation α+α−1=β+β−1. In this paper we use new techniques (which are useful in noncommutative situations as well) to provide alternate proofs of the results:- If α,β commute then there is a central projection p in M such that α=β on MP and α=β−1 on M(1−P); If M=B(H), the algebra of all bounded operators on a Hilbert space H, then α=β or α=β−1.http://dx.doi.org/10.1155/S0161171286000923automorphismscentral projectionHilbert-Schmidt operators. |
| spellingShingle | A. B. Thaheem On the operator equation α+α−1=β+β−1 International Journal of Mathematics and Mathematical Sciences automorphisms central projection Hilbert-Schmidt operators. |
| title | On the operator equation α+α−1=β+β−1 |
| title_full | On the operator equation α+α−1=β+β−1 |
| title_fullStr | On the operator equation α+α−1=β+β−1 |
| title_full_unstemmed | On the operator equation α+α−1=β+β−1 |
| title_short | On the operator equation α+α−1=β+β−1 |
| title_sort | on the operator equation α α 1 β β 1 |
| topic | automorphisms central projection Hilbert-Schmidt operators. |
| url | http://dx.doi.org/10.1155/S0161171286000923 |
| work_keys_str_mv | AT abthaheem ontheoperatorequationaa1bb1 |