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Seminormed ⁎-subalgebras of ℓ∞(X)
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- Alaghmandan, Mahmood, 1983 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, Analys och sannolikhetsteori,Department of Mathematical Sciences, Analysis and Probability Theory
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- Ghasemi, Mehdi (author)
- University of Saskatchewan
- (creator_code:org_t)
- Elsevier BV, 2017
- 2017
- English.
- In: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 455:1, s. 212-220
- Journal article (peer-reviewed)
Abstract
Subject headings
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- Arbitrary representations of an involutive commutative unital F-algebra A as a subalgebra of FX are considered, where F=C or R and X≠∅. The Gelfand spectrum of A is explained as a topological extension of X where a seminorm on the image of A in FX is present. It is shown that among all seminorms, the sup-norm is of special importance which reduces FX to ℓ∞(X). The Banach subalgebra of ℓ∞(X) of all Σ-measurable bounded functions on X, Mb(X,Σ), is studied for which Σ is a σ-algebra of subsets of X. In particular, we study lifting of positive measures from (X,Σ) to the Gelfand spectrum of Mb(X,Σ) and observe an unexpected shift in the support of measures. In the case that Σ is the Borel algebra of a topology, we study the relation of the underlying topology of X and the topology of the Gelfand spectrum of Mb(X,Σ).
Subject headings
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Keyword
- Measures on Boolean rings
- Gelfand spectrum
- Function algebras
- Measurable functions
- Commutative normed algebras
- Seminormed algebras
- Commutative normed algebras
- Function algebras
- Gelfand spectrum
- Measurable functions
- Measures on Boolean rings
- Seminormed algebras
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- art (subject category)
- ref (subject category)
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- Chalmers University of Technology
- University of Gothenburg
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