An Extension of the Spectral Mapping Theorem

A. R. Medghalchi and S. M. Tabatabaie

International Journal of Mathematics and Mathematical Sciences, 2008, vol. 2008, 1-8

Abstract:

We give an extension of the spectral mapping theorem on hypergroups and prove that if ð ¾ is a commutative strong hypergroup with 0 ð ‘¥ 0 0 0 5 ð ‘’ ð ¾ = ð ‘‹ ð ‘ ( ð ¾ ) and 𠜅 is a weakly continuous representation of ð ‘€ ( ð ¾ ) on a ð ‘Š ∗ -algebra such that for every ð ‘¡ ∈ ð ¾ , 𠜅 ð ‘¡ is an ∗ -automorphism, ð ‘ ð ‘ ð œ… is a synthesis set for ð ¿ 1 ( ð ¾ ) and 𠜅 ( ð ¿ 1 ( ð ¾ ) ) is without order, then for any 𠜇 in a closed regular subalgebra of ð ‘€ ( ð ¾ ) containing ð ¿ 1 ( ð ¾ ) , 𠜎 ( 𠜅 ( 𠜇 ) ) = 0 ð ‘¥ 0 0 0 5 ð ‘’ 𠜇 ( ð ‘ ð ‘ ð œ… ) , where ð ‘ ð ‘ ð œ… is the Arveson spectrum of 𠜅 .

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:531424

DOI: 10.1155/2008/531424

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