2018/04/29 by Mahya Ghandehari, Ghandehari, Mahya
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA
paper · pdf · doi:10.48550/arxiv.1804.10937
16 pages
arxiv created 2018/04/29 · openalex publication_date 2018/04/29 · arxiv updated 2018/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a locally compact Abelian group G, the algebra of Rajchman measures, denoted by M0(G), is the set of all bounded regular Borel measures on G whose Fourier transform vanish at infinity. In this paper, we investigate the spectral structure of the algebra of Rajchman measures, and illustrate aspects of the residual analytic structure of its maximal ideal space. In particular, we show that M0(G) has a nonzero continuous point derivation, whenever G is a non-discrete locally compact Abelian group. We then give the definition of the Rajchman algebra for a general (not necessarily Abelian) locally compact group, and prove that for a non-compact connected SIN group, the Rajchman algebra admits a nonzero continuous point derivation. Moreover, we discuss the analytic behavior of the spectrum of M0(G). Namely, we show that for every non-discrete metrizable locally compact Abelian group G, the maximal ideal space of M0(G) contains analytic discs.