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We study contraction groups for automorphisms of totally disconnected locally compact groups using the scale of the automorphism as a tool. The contraction group is shown to be unbounded when the… (More)

- George A. Willis
- 2001

A new characterisation of the scale function on the locally compact group G is given. It is shown that for x in G the scale of x, s(x), is the minimum value attained by the index [xUx− 1 : xUx− 1 ∩… (More)

- George A. Willis
- 1992

It is shown how to construct, given a Banach space which does not have the approximation property, another Banach space which does not have the approximation property but which does have the compact… (More)

- George A. Willis
- 2013

The scale of an endomorphism, $$\alpha $$α, of a totally disconnected, locally compact group $$G$$G is the minimum index $$[\alpha (U) : \alpha (U)\cap U]$$[α(U):α(U)∩U], for $$U$$U a compact, open… (More)

For a Banach algebra A, amenability of A∗∗ necessitates amenability of A, and similarly for weak amenability provided A is a left ideal in A∗∗. For G a locally compact group, indeed more generally,… (More)

The invention relates to a power transmission belt having a circumferentially ribbed inner surface. According to the invention, the sides (42) of each rib (38) join a small base (40) of the rib via… (More)

- George A. Willis
- 2004

Let α be an automorphism of the totally disconnected group G. The compact open subgroup, V ,o fG is tidy for α if (α(V ): α(V ) ∩ V ) is minimised at V , where V ranges over all compact open… (More)

Let G be a totally disconnected, locally compact group admitting a contractive automorphism f. We prove a Jordan-Holder theorem for series of f-stable closed subgroups of G, classify all possible… (More)

- George A. Willis
- 1990

Abstract Let G be a locally compact group. Random walks on G , some factorization problems in L 1 ( G ) and the significance for these of the amenability of G are studied. These topics are linked in… (More)

The paper establishes a substantial number of cases of a conjecture regarding commensurated subgroups of S-arithmetic groups made by Margulis and Zimmer in the late 1970s. New results in the… (More)