Seminormed ⁎-subalgebras of ℓ∞(X)
Artikel i vetenskaplig tidskrift, 2017

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).

Seminormed algebras

Commutative normed algebras

Function algebras

Measures on Boolean rings

Gelfand spectrum

Measurable functions

Författare

Mahmood Alaghmandan

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Mehdi Ghasemi

University of Saskatchewan

Journal of Mathematical Analysis and Applications

0022-247X (ISSN) 1096-0813 (eISSN)

Vol. 455 1 212-220

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

DOI

10.1016/j.jmaa.2017.05.041

Mer information

Senast uppdaterat

2018-03-29