Spectra of Abelian C*-Subalgebra Sums

2014/09/18 by Christian Fleischhack, Fleischhack, Christian
Mathematics · Physics and Astronomy · #46J40 (Primary) #46L05 #54A10 #54C50 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #math-ph #math.FA #math.MP #math.OA #msc:46J40 #msc:46L05 #msc:54A10 #msc:54C50

paper · pdf · doi:10.48550/arxiv.1409.5273

12 pages, LaTeX. Extension of Section 3 in arXiv:1010.0449 (version v1)

arxiv created 2014/09/18 · arxiv updated 2014/09/19

Abstract

Let C_b(X) be the C*-algebra of bounded continuous functions on some non-compact, but locally compact Hausdorff space X. Moreover, let A₀ be some ideal and A₁ be some unital C*-subalgebra of C_b(X). For A₀ and A₁ 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 before. 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.

Citations

• Loop Quantization and Symmetry: Configuration Spaces

Related

• A Semigroup Composition C*-algebra
• C^*-bialgebra defined as the direct sum of UHF algebras
• Representation of spectrums of C^∗-algebras of bounded functions in terms of filters
• Character Space and Gelfand type representation of locally C^*-algebra
• A Mayer-Vietoris Spectral Sequence for C*-Algebras and Coarse Geometry