Abstract
Let A be a C0(X)algebra with continuous map φ from Prim(A), the primitive ideal space of A, to a locally compact Hausdorff space X. Then the multiplier algebra M(A) is a C(β X)algebra with continuous map Graphic: Prim(M(A)) → β X extending φ. For x ∈ Im(φ), let Jx = ⋂{P ∈ Prim(A): φ(P) = x} and Graphic. Then Graphic, the strict closure of Jx in M(A). Thus, Hx is strictly closed if and only if Graphic, and the ‘spectral synthesis’ question asks when this happens. In this paper, it is shown that, for σunital A, Hx is strictly closed for all x ∈ Im(φ) if and only if Jx is locally modular for all x ∈ Im(φ) and φ is a closed map relative to its image. Various related results are obtained.
Original language  English 

Pages (fromto)  124 
Number of pages  24 
Journal  Quarterly Journal of Mathematics 
Volume  65 
Issue number  1 
Early online date  22 Jan 2013 
DOIs  
Publication status  Published  1 Mar 2014 
Bibliographical note
We are grateful to the referee for a number of helpful comments and for pointing out an error in the original proof of Theorem 3.6.Fingerprint
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Robert Archbold
 School of Natural & Computing Sciences, Mathematical Science  Emeritus Professor
Person: Honorary