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Seminormed ⁎-subalgebras of ℓ∞(X)

Mahmood Alaghmandan (Institutionen för matematiska vetenskaper, Analys och sannolikhetsteori) ; Mehdi Ghasemi
Journal of Mathematical Analysis and Applications (0022247X). Vol. 455 (2017), 1, p. 212-220.
[Artikel, refereegranskad vetenskaplig]

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).

Nyckelord: Commutative normed algebras; Function algebras; Gelfand spectrum; Measurable functions; Measures on Boolean rings; Seminormed algebras

Denna post skapades 2017-10-04.
CPL Pubid: 252316


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Institutionen för matematiska vetenskaper, Analys och sannolikhetsteoriInstitutionen för matematiska vetenskaper, Analys och sannolikhetsteori (GU)


Matematisk analys
Algebra och logik

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