International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 531424, 8 pages
Research Article

An Extension of the Spectral Mapping Theorem

A. R. Medghalchi1 and S. M. Tabatabaie2

1Faculty of Mathematical Sciences and Computer Engineering, Tabbiat Moallem University, Tehran 15618, Iran
2Department of Mathematics, The University of Qom, Qom 3716146611, Iran

Received 8 January 2008; Accepted 4 May 2008

Academic Editor: Ingo Witt

Copyright © 2008 A. R. Medghalchi and S. M. Tabatabaie. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We give an extension of the spectral mapping theorem on hypergroups and prove that if K is a commutative strong hypergroup with K^=Xb(K) and κ is a weakly continuous representation of M(K) on a W-algebra such that for every tK, 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))=μ^(spκ)¯, where spκ is the Arveson spectrum of κ.