Work

Non-separability of the Gelfand space of measure algebras

Year: 2016

Type: article

Abstract: 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 M0(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.

Source: Arkiv för matematik

DOI: 10.1007/s11512-016-0240-8

Authors: Przemysław Ohrysko, Michał Wojciechowski, Colin C. Graham

Institutions: Institute of Mathematics, Polish Academy of Sciences, University of British Columbia

Language: Swedish

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Narodowym Centrum Nauki

OpenAlex ID: W2394690339