Thursday, 23 February 2023

### 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.

Joint work with P. Ohrysko, and C. Graham.

Speaker

Michał Wojciechowski

Research area

Analysis seminar

Affilation

UNSW

Date

Thursday 23 February 2023, 2:00 pm

Location

RC-4082