Non-separability of the Gelfand space of measure algebras
Autor: | Colin C. Graham, Michał Wojciechowski, Przemysław Ohrysko |
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Rok vydání: | 2016 |
Předmět: |
Pure mathematics
General Mathematics 010102 general mathematics 02 engineering and technology Disjoint sets 01 natural sciences Measure (mathematics) Functional Analysis (math.FA) Separable space Mathematics - Functional Analysis FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Measure algebra Countable set 020201 artificial intelligence & image processing Ideal (order theory) Locally compact space 0101 mathematics Abelian group Mathematics |
Zdroj: | Ark. Mat. 54, no. 2 (2016), 525-535 |
ISSN: | 0004-2080 |
Popis: | We prove that there exists uncountably many pairwise disjoint open subsets of the Gelfand space of the measure algebra on any locally compact non-discrete abelian group which shows that this space is not separable (in fact, we prove this assertion for the ideal $M_{0}(G)$ consisting of measures with Fourier-Stieltjes transforms vanishing at infinity which is a stronger statement). As a corollary, we obtain that the spectras of elements in the algebra of measures cannot be recovered from the image of one countable subset of the Gelfand space under Gelfand transform, common for all elements in the algebra. |
Databáze: | OpenAIRE |
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