Search

Only show content I have access to (0)

Articles (1)

Over 3 years (1)

From year:

To year:

Apply

Mathematics (1)

Proceedings of the Edinburgh Mathematical Society (1)

1 results

The Spectra of Algebras of Group-Symmetric Functions
Part of
- Linear function spaces and their duals
- Measures, integration, derivative, holomorphy
Domingo García, Manuel Maestre, Ignacio Zalduendo
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 62 / Issue 3 / August 2019

Published online by Cambridge University Press:

29 November 2018, pp. 609-623
- Article
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation
In the study of the spectra of algebras of holomorphic functions on a Banach space E, the bidual E″ has a central role, and the spectrum is often shown to be locally homeomorphic to E″. In this paper we consider the problem of spectra of subalgebras invariant under the action of a group (functions f such that f ○ g = f). It is natural to attempt a characterization in terms of the space of orbits E″/~ obtained from E″ through the action of the group, so we pursue this approach here and introduce an analytic structure on the spectrum in some situations. In other situations we encounter some obstacles: in some cases, the lack of structure of E″/~ itself; in others, problems of weak continuity and non-approximability of functions in the algebra. We also define a convolution operation related to the spectrum.