2013/05/24 by Rui Palma, Palma, Rui
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Group Theory (math.GR) #Operator Algebras (math.OA) #math.FA #math.GR #math.OA
paper · pdf · doi:10.48550/arxiv.1305.5852
22 pages
arxiv created 2013/05/24 · openalex publication_date 2013/05/24 · arxiv updated 2013/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A locally compact group G is said to be Hermitian if every selfadjoint element of L1(G) has real spectrum. Using Halmos' notion of capacity in Banach algebras and a result of Jenkins, Fountain, Ramsay and Williamson we will put a bound on the growth of Hermitian groups. In other words, we will show that if G has a subset that grows faster than a certain constant, then G cannot be Hermitian. Our result allows us to give new examples of non-Hermitian groups which could not tackled by the existing theory. The examples include certain infinite free Burnside groups, automorphism groups of trees, and p-adic general and special linear groups.