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Vietnam Journal of Mathematics

, Volume 47, Issue 1, pp 195–208 | Cite as

Spectra of Abelian C-Subalgebra Sums

  • Christian FleischhackEmail author
Article
  • 7 Downloads

Abstract

Let Cb(X) be the C-algebra of bounded continuous functions on some non-compact, but locally compact Hausdorff space X. Moreover, let \(\mathfrak {A}_{0}\) be some ideal and \(\mathfrak {A}_{1}\) be some unital C-subalgebra of Cb(X). For \(\mathfrak {A}_{0}\) and \(\mathfrak {A}_{1}\) having trivial intersection, we show that the spectrum of their vector space sum equals the disjoint union of their individual spectra, whereas their topologies are nontrivially interwoven. Indeed, they form a so-called twisted-sum topology which we will investigate beforehand. Within the whole framework, e.g., the one-point compactification of X and the spectrum of the algebra of asymptotically almost periodic functions can be described.

Keywords

Spectra of abelian C-algebras Twisted-sum topology Asymptotically almost periodic functions Mathematical foundations of loop quantum cosmology 

Mathematics Subject Classification (2010)

46J40 (Primary) 46L05 54A10 54C50 (Secondary) 

Notes

Acknowledgements

The author thanks Maximilian Hanusch for numerous discussions and many helpful comments on a draft of the present article. Moreover, the author gratefully acknowledges discussions with Thomas Tonev concerning asymptotically almost periodic functions. The author has been supported by the Emmy-Noether-Programm of the Deutsche Forschungsgemeinschaft under grant FL 622/1-1.

Funding Information

The author has been supported by the Emmy-Noether-Programm of the Deutsche Forschungsgemeinschaft under grant FL 622/1-1.

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Institut für MathematikUniversität PaderbornPaderbornGermany

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