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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |