File(s) not publicly available
The spectral theory of commutative C*-algebras: the constructive spectrum
journal contribution
posted on 2023-06-07, 21:40 authored by Bernhard Banaschewski, Christopher J MulveyThis paper introduces the notion of a commutative C*-algebra in a Grothendieck topos E and subsequently that of the spectrum MFn A of A, presented as the locale determined by an appropriate propositional theory in the topos E which describes the basic properties of a multplicative linear functional on A. Further, the locale CE of complex numbers in the topos E is defined in a similar manner and some of its basic properties are established, such as its complete regularity and the compactness of the unit square in CE. Finally, it is shown that the locale MFn A is compact and completely regular, extending the classical result that the multiplicative linear functionals on a commutative C*-algebra form a compact Hausdorff space in the weak* topology.
History
Publication status
- Published
Journal
Quaestiones MathematicaeISSN
1607-3606Publisher
Taylor and FrancisExternal DOI
Issue
4Volume
23Page range
425-464ISBN
1607-3606Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
Categories
No categories selectedLicence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC