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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 inverse automorphism has non-trivial scale and this scale is shown to be the inverse value of the modular function on the closure of the contraction group at the… (More)

Let α be an automorphism of the totally disconnected group G. The compact open subgroup, V , of G is tidy for α if [α(V ) : α(V ) ∩ V ] is minimised at V , where V ′ ranges over all compact open subgroups of G. Identifying a subgroup tidy for α is analogous to identifying a basis which puts a linear transformation into Jordan canonical form. This analogy is… (More)

- G. A. Willis, G. A. WILLIS
- 1994

In this paper we study conditions on a Banach space X that ensure that the Banach algebra K(X) of compact operators is amenable. We give a symmetrized approximation property of X which is proved to be such a condition. This property is satisfied by a wide range of Banach spaces including all the classical spaces. We then investigate which constructions of… (More)

- George Willis
- 2008

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 approximation property. 1991 Mathematics Subject Classification: primary 46B28; secondary 46B10

- Frank P Cuozzo, Michelle L Sauther, +13 authors George Willis
- American journal of primatology
- 2008

Chemical deterioration of teeth is common among modern humans, and has been suggested for some extinct primates. Dental erosion caused by acidic foods may also obscure microwear signals of mechanical food properties. Ring-tailed lemurs at the Beza Mahafaly Special Reserve (BMSR), Madagascar, display frequent severe tooth wear and subsequent tooth loss. In… (More)

- Helge Glöckner, George A. Willis
- 2006

Let G be a totally disconnected, locally compact group admitting a contractive automorphism α. We prove a Jordan-Hölder theorem for series of α-stable closed subgroups of G, classify all possible composition factors and deduce consequences for the structure of G. Classification: 22D05 (primary); 20E15, 20E36

The flat rank of a totally disconnected locally compact group G, denoted flat-rk(G), is an invariant of the topological group structure of G. It is defined thanks to a natural distance on the space of compact open subgroups of G. For a topological Kac-Moody group G with Weyl group W , we derive the inequalities: alg-rk(W ) ≤ flat-rk(G) ≤ rk(|W |0). Here,… (More)

The Margulis-Zimmer conjecture. The subject of this paper is a well known question advertised by Gregory Margulis and Robert Zimmer since the late 1970’s, which seeks refinement of the celebrated Normal Subgroup Theorem of Margulis (hereafter abbreviated NST). Although Margulis’ NST is stated and proved in the context of (higher rank) irreducible lattices… (More)

- GEORGE A. WILLIS
- 2006

We consider locally compact groups G admitting a topologically transitive Z -action by automorphisms. It is shown that such a group G has a compact normal subgroupK ofG, invariant under the action, such thatG/K is a product of (finitely many) locally compact fields of characteristic zero; moreover, the totally disconnected fields in the decomposition can be… (More)

- Corey Heitz, Melanie Prusakowski, George Willis, Christopher Franck
- The western journal of emergency medicine
- 2015

INTRODUCTION
Linking educational objectives and clinical learning during clerkships can be difficult. Clinical shifts during emergency medicine (EM) clerkships provide a wide variety of experiences, some of which may not be relevant to recommended educational objectives. Students can be directed to standardize their clinical experiences, and this improves… (More)