An Extension of the Spectral Mapping Theorem
We give an extension of the spectral mapping theorem on hypergroups and prove that if 𝐾 is a commutative strong hypergroup with 0𝑥0005𝑒𝐾=𝑋𝑏(𝐾) and 𝜅 is a weakly continuous representation of 𝑀(𝐾) on a 𝑊∗-algebra such that for every 𝑡∈𝐾, 𝜅𝑡 is an ∗-automorphism, 𝑠𝑝𝜅 is a synthesis set for 𝐿1(𝐾) and 𝜅(...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/531424 |
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| author | A. R. Medghalchi S. M. Tabatabaie |
| author_facet | A. R. Medghalchi S. M. Tabatabaie |
| author_sort | A. R. Medghalchi |
| collection | DOAJ |
| description | We give an extension of the spectral mapping theorem
on hypergroups and prove that if 𝐾 is a commutative strong hypergroup with 0𝑥0005𝑒𝐾=𝑋𝑏(𝐾) and 𝜅 is a weakly continuous representation of 𝑀(𝐾) on a 𝑊∗-algebra such that for every 𝑡∈𝐾, 𝜅𝑡 is an ∗-automorphism, 𝑠𝑝𝜅 is a synthesis
set for 𝐿1(𝐾) and 𝜅(𝐿1(𝐾)) is without order, then for any 𝜇 in a closed regular
subalgebra of 𝑀(𝐾) containing 𝐿1(𝐾), 𝜎(𝜅(𝜇))=0𝑥0005𝑒𝜇(𝑠𝑝𝜅), where 𝑠𝑝𝜅 is the
Arveson spectrum of 𝜅. |
| format | Article |
| id | doaj-art-3072c402f7194354b83155ea55ed2030 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3072c402f7194354b83155ea55ed20302025-02-03T06:08:17ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/531424531424An Extension of the Spectral Mapping TheoremA. R. Medghalchi0S. M. Tabatabaie1Faculty of Mathematical Sciences and Computer Engineering, Tabbiat Moallem University, Department of Mathematics, The University of Qom, Qom 3716146611, IranWe give an extension of the spectral mapping theorem on hypergroups and prove that if 𝐾 is a commutative strong hypergroup with 0𝑥0005𝑒𝐾=𝑋𝑏(𝐾) and 𝜅 is a weakly continuous representation of 𝑀(𝐾) on a 𝑊∗-algebra such that for every 𝑡∈𝐾, 𝜅𝑡 is an ∗-automorphism, 𝑠𝑝𝜅 is a synthesis set for 𝐿1(𝐾) and 𝜅(𝐿1(𝐾)) is without order, then for any 𝜇 in a closed regular subalgebra of 𝑀(𝐾) containing 𝐿1(𝐾), 𝜎(𝜅(𝜇))=0𝑥0005𝑒𝜇(𝑠𝑝𝜅), where 𝑠𝑝𝜅 is the Arveson spectrum of 𝜅.http://dx.doi.org/10.1155/2008/531424 |
| spellingShingle | A. R. Medghalchi S. M. Tabatabaie An Extension of the Spectral Mapping Theorem International Journal of Mathematics and Mathematical Sciences |
| title | An Extension of the Spectral Mapping Theorem |
| title_full | An Extension of the Spectral Mapping Theorem |
| title_fullStr | An Extension of the Spectral Mapping Theorem |
| title_full_unstemmed | An Extension of the Spectral Mapping Theorem |
| title_short | An Extension of the Spectral Mapping Theorem |
| title_sort | extension of the spectral mapping theorem |
| url | http://dx.doi.org/10.1155/2008/531424 |
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