2016/12/25 by Fouad Naderi, Naderi, Fouad · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology #math.FA
paper · pdf · doi:10.48550/arxiv.1612.08286
We uses a different method to prove that if the reduced Fourier-Stieltjes algebra has weak* fpp, then the group is compact. Also, a counter example to Randrianantoanina is provided
openalex publication_date 2016/12/25 · arxiv created 2017/01/28 · arxiv updated 2017/01/31 · openalex created_date 2017/02/10 · openalex updated_date 2026/07/28
In this paper, we show that if the reduced Fourier-Stieltjes algebra Bρ(G) of a second countable locally compact group G has either weak* fixed point property or asymptotic center property, then G is compact. As a result, we give affirmative answers to open problems raised by Fendler and et al. in 2013. We then conclude that a second countable group with a discrete reduced dual must be compact. This generalizes a theorem of Baggett. We also construct a compact scattered Hausdorff space Ω for which the dual of the scattered C*-algebra C(Ω) lacks weak* fixed point property. The C*-algebra C(Ω) provides a negative answer to a question of Randrianantoanina in 2010. In addition, we prove a variant of Bruck's generalized fixed point theorem for the preduals of von Neumann algebras. Furthermore, we give some examples emphasizing that the conditions in Bruck's generalized conjecture (BGC) can not be weakened any more.