Geodesic
On the growth of Hermitian groups
Rui Palma1
1University of Oslo, Norway
Groups, geometry, and dynamics, Tome 9 (2015) no. 1, pp. 29-53

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DOI

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.
DOI : 10.4171/ggd/304
Classification : 20-XX, 22-XX, 43-XX
Mots-clés : Hermitian group, growth rate of groups

Rui Palma  1

1 University of Oslo, Norway 
Rui Palma. On the growth of Hermitian groups. Groups, geometry, and dynamics, Tome 9 (2015) no. 1, pp. 29-53. doi: 10.4171/ggd/304
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