2021 
Glöckner H, Willis GA, 'Decompositions of locally compact contraction groups, series and extensions', Journal of Algebra, 570 164214 (2021)
© 2020 Elsevier Inc. A locally compact contraction group is a pair (G,a), where G is a locally compact group and a:G¿G an automorphism such that an(x)¿e pointwise as n¿8. We show ... [more]
© 2020 Elsevier Inc. A locally compact contraction group is a pair (G,a), where G is a locally compact group and a:G¿G an automorphism such that an(x)¿e pointwise as n¿8. We show that every surjective, continuous, equivariant homomorphism between locally compact contraction groups admits an equivariant continuous global section. As a consequence, extensions of locally compact contraction groups with abelian kernel can be described by continuous equivariant cohomology. For each prime number p, we use 2cocycles to construct uncountably many pairwise nonisomorphic totally disconnected, locally compact contraction groups (G,a) which are central extensions {0}¿Fp((t))¿G¿Fp((t))¿{0} of the additive group of the field of formal Laurent series over Fp=Z/pZ by itself. By contrast, there are only countably many locally compact contraction groups (up to isomorphism) which are torsion groups and abelian, as follows from a classification of the abelian locally compact contraction groups.



2020 
Groenhout P, Reid CD, Willis GA, 'Topologically simple, totally disconnected, locally compact infinite matrix groups', Journal of Lie Theory, 30 965980 (2020)
© 2020 Heldermann Verlag We construct uncountably many nonlocally isomorphic examples of topologically simple nondiscrete totally disconnected locally compact groups. The new exa... [more]
© 2020 Heldermann Verlag We construct uncountably many nonlocally isomorphic examples of topologically simple nondiscrete totally disconnected locally compact groups. The new examples differ from known examples of such groups in that they have trivial quasicentre, but also have infinite abelian locally normal subgroups. The examples are constructed as almost uppertriangular matrices modulo scalar matrices over finite fields, where 'almost uppertriangular' is defined with respect to one of an uncountable family of preorders generalising the orders (Z, =) and (N, =).



2020 
Carter MAX, Willis GA, 'DECOMPOSITION THEOREMS for AUTOMORPHISM GROUPS of TREES', Bulletin of the Australian Mathematical Society, (2020)
© 2020 Australian Mathematical Publishing Association Inc. Motivated by the Bruhat and Cartan decompositions of general linear groups over local fields, we enumerate double cosets... [more]
© 2020 Australian Mathematical Publishing Association Inc. Motivated by the Bruhat and Cartan decompositions of general linear groups over local fields, we enumerate double cosets of the group of labelpreserving automorphisms of a labelregular tree over the fixator of an end of the tree and over maximal compact open subgroups. This enumeration is used to show that every continuous homomorphism from the automorphism group of a labelregular tree has closed range.



2020 
Carter M, Tornier S, Willis G, 'On free products of graphs', Australasian Journal of Combinatorics, 78 154176 (2020) [C1]



2020 
Ghahramani F, Loy RJ, Willis GA, 'ADDENDUM TO "AMENABILITY AND WEAK AMENABILITY OF SECOND CONJUGATE BANACH ALGEBRAS"', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 148 45734575 (2020)



2020 
Praeger CE, Ramagge J, Willis GA, 'A graphtheoretic description of scalemultiplicative semigroups of automorphisms', Israel Journal of Mathematics, 237 221265 (2020) [C1]



2018 
Willis GA, 'Homological properties of the Algebra of compact operators on a banach space', Rocky Mountain Journal of Mathematics, 48 687701 (2018) [C1]



2017 
Willis GA, 'THE SCALE FUNCTION AND LATTICES', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 145 31853190 (2017) [C1]



2017 
Caprace PE, Reid CD, Willis GA, 'LOCALLY NORMAL SUBGROUPS OF TOTALLY DISCONNECTED GROUPS. PART I: GENERAL THEORY', FORUM OF MATHEMATICS SIGMA, 5 (2017) [C1]



2017 
Caprace PE, Reid CD, Willis GA, 'LOCALLY NORMAL SUBGROUPS OF TOTALLY DISCONNECTED GROUPS. PART II: COMPACTLY GENERATED SIMPLE GROUPS', FORUM OF MATHEMATICS SIGMA, 5 (2017) [C1]



2017 
Willis GA, 'Computing the scale of an endomorphism of a totally disconnected locally compact group', Axioms, 6 (2017) [C1]



2016 
Baumgartner U, Ramagge J, Willis GA, 'Scalemultiplicative semigroups and geometry: Automorphism groups of trees', Groups, Geometry, and Dynamics, 10 10511075 (2016) [C1]
© European Mathematical Society. A scalemultiplicative semigroup in a totally disconnected, locally compact group G is one for which the restriction of the scale function on G is... [more]
© European Mathematical Society. A scalemultiplicative semigroup in a totally disconnected, locally compact group G is one for which the restriction of the scale function on G is multiplicative The maximal scalemultiplicative semigroups in groups acting 2transitively on the set of ends of trees without leaves are determined and shown to correspond to geometric features of the tree.



2015 
Willis GA, 'The scale and tidy subgroups for endomorphisms of totally disconnected locally compact groups', MATHEMATISCHE ANNALEN, 361 403442 (2015) [C1]



2015 
Banks C, Elder M, Willis GA, 'Simple groups of automorphisms of trees determined by their actions on finite subtrees', JOURNAL OF GROUP THEORY, 18 235261 (2015) [C1]



2015 
Hofmann KH, Willis GA, 'Continuity Characterizing Totally Disconnected Locally Compact Groups', JOURNAL OF LIE THEORY, 25 17 (2015) [C1]



2014 
Caprace PE, Reid CD, Willis GA, 'Limits of contraction groups and the tits core', Journal of Lie Theory, 24 957967 (2014) [C1]



2014 
Willis GA, 'The nub of an automorphism of a totally disconnected, locally compact group', Ergodic Theory and Dynamical Systems, 34 13651394 (2014) [C1]



2013 
Shalom Y, Willis GA, 'Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity', GEOMETRIC AND FUNCTIONAL ANALYSIS, 23 16311683 (2013) [C1]



2013 
Caprace PE, Reid CD, Willis GA, 'Locally normal subgroups of simple locally compact groups', Comptes Rendus Mathematique, 351 657661 (2013) [C1]



2012 
Baumgartner U, Moller RG, Willis GA, 'Hyperbolic groups have flatrank at most 1', Israel Journal of Mathematics, 190 365388 (2012) [C1]



2012 
Willis GA, 'Probability measures on semigroups: Convolution products, random walks and random matrices [Book Review]', SIAM Review, 54 414416 (2012) [C3] 


2010 
Baumgartner U, Schlichting G, Willis GA, 'Geometric characterization of flat groups of automorphisms', Groups, Geometry, and Dynamics, 4 113 (2010) [C1]



2010 
Ghahramani F, Read CJ, Willis GA, 'Closed ideal structure and cohomological properties of certain radical Banach algebras', Proceedings of the London Mathematical Society, 100 533559 (2010) [C1]



2010 
Glockner H, Willis GA, 'Classification of the simple factors appearing in composition series of totally disconnected contraction groups', Journal Fur Die Reine Und Angewandte Mathematik, 141169 (2010) [C1]



2009 
Baumgartner U, Laca M, Ramagge J, Willis GA, 'Hecke algebras from groups acting on trees and HNN extensions', Journal of Algebra, 321 30653088 (2009) [C1]



2007 
Baumgartner U, Remy B, Willis GA, 'Flat rank of automorphism groups of buildings', Transformation Groups, 12 413436 (2007) [C1]



2007 
Glockner H, Willis GA, 'Directions of automorphisms of Lie groups over local fields compared to the directions of Lie algebra automorphisms', Topology Proceedings, 31 481501 (2007) 


2007 
Willis GA, 'Compact open subgroups in simple totally disconnected groups', Journal of Algebra, 312 405417 (2007) [C1]



2006 
Dani SG, Shah NA, Willis GA, 'Locally compact groups with dense orbits under Z(d)actions by automorphisms', Ergodic Theory and Dynamical Systems, 26 14431465 (2006) [C1]



2006 
Baumgartner U, Willis GA, 'The direction of an automorphism of a totally disconnected locally compact group', Mathematische Zeitschrift, 252 393428 (2006) [C1]



2006 
Baumgartner U, Ramagge J, Willis GA, 'A compactly generated group whose Hecke algebras admit no bounds on their representations', Glasgow Mathematical Journal, 48 193201 (2006) [C1]



2004 
Willis GA, 'A noncommutative halfangle formula', Bulletin of Australian Mathematical Society, 69 369382 (2004) [C1]



2004 
Abdollahi A, Rejali A, Willis GA, 'Group Properties characterised by configurations', Illinois Journal of Mathematics, 48 861873 (2004) [C1]



2004 
Baumgartner U, Willis GA, 'Contraction groups and scales of automorphisms of totally disconnected locally compact groups', Israel Journal of Mathematics, 142 221248 (2004) [C1]



2004 
Willis GA, 'Tidy subgroups for commuting automorphisms of totally disconnected groups: An analogue of simultaneous triangularisation of Matrices', New York Journal of Mathematics, 10 135 (2004) [C1]



2001 
Glockner H, Willis GA, 'Uniscalar padic Lie groups', FORUM MATHEMATICUM, 13 413421 (2001) [C1]



2001 
Rosenblatt JM, Willis GA, 'Weak convergence is not strong convergence for amenable groups', Canadian Math. Bull., 44 231241 (2001) [C1]



2001 
Willis GA, 'Further properties of the scale function on a totally disconnected group', Journal of Algebra, 237 142164 (2001) [C1]



2001 
Willis GA, 'The number of prime factors of the scale function on a compactly generated group is finite', Bulletin London Mathematical Society, 33 168174 (2001) [C1]



2001 
Willis GA, 'Factorization in finitecodimensional ideals of group algebras', Proc. London Math. Soc., 82 676700 (2001) [C1]



2001 
Kepert AG, Willis G, 'Scale Functions and Tree Ends', Journal of Australian Mathematics Society, 70 273292 (2001) [C1]



2000 
Willis GA, Loy RJ, Read CJ, Runde V, 'Amenable and weakly amenable Banach algebras with compact multiplication', Journal of Functional Analysis, 171 78114 (2000) [C1]



2000 
Willis GA, Ghahramani F, Runde V, 'Derivations on Group Algebras', Proceedings of the London Mathematical Society, 80 360390 (2000) [C1]



2000 
Willis GA, 'An extension of a noncommutative ChoquetDeny Theorem', Proceedings of the American Mathematical Society, 128 111118 (2000) [C1]



1997 
Willis G, 'Totally disconnected, nilpotent, locally compact groups', BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 55 143146 (1997)



1997 
Gronbaek N, Willis GA, 'Embedding nilpotent finite dimensional Banach algebras into amenable Banach algebras', JOURNAL OF FUNCTIONAL ANALYSIS, 145 99107 (1997)



1997 
Ross KA, Willis G, 'Riemann sums and modular functions on locally compact groups', PACIFIC JOURNAL OF MATHEMATICS, 180 325331 (1997)



1996 
Ghahramani F, Loy RJ, Willis GA, 'Amenability and weak amenability of second conjugate Banach algebras', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 124 14891497 (1996)



1996 
Jaworski W, Rosenblatt J, Willis G, 'Concentration functions in locally compact groups', MATHEMATISCHE ANNALEN, 305 673691 (1996)



1996 
Lau ATM, Loy RJ, Willis GA, 'Amenability of Banach and C*algebras on locally compact groups', STUDIA MATHEMATICA, 119 161178 (1996)



1995 
Willis GA, 'When the algebra generated by an operator is amenable', Journal of Operator Theory, 34 239250 (1995) 


1995 
WILLIS G, 'TOTALLY DISCONNECTED GROUPS AND PROOFS OF CONJECTURES OF HOFMANN AND MUKHERJEA', BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 51 489494 (1995)



1995 
WILLIS GA, 'COMPRESSIBLE OPERATORS AND THE CONTINUITY OF HOMOMORPHISMS FROM ALGEBRAS OF OPERATORS', STUDIA MATHEMATICA, 115 251259 (1995)



1994 
Sitaram A, Willis GA, 'LpFunctions Satisfying the Mean Value Property on Homogeneous Spaces', Journal of the Australian Mathematical Society, 56 384390 (1994)
It is proved That on certain kINDs of homogeneous Spaces, The only Lpfunction, 1 < p < oo, satisfying the mean value property is the zero function. 1991 Mathematics subject ... [more]
It is proved That on certain kINDs of homogeneous Spaces, The only Lpfunction, 1 < p < oo, satisfying the mean value property is the zero function. 1991 Mathematics subject classification (Amer: Math. Soc.): 22 E 99,43 A 85. © 1994, Australian Mathematical Society. All rights reserved.



1994 
Willis G, 'Factorization in Banach algebras', Linear and Complex Analyisis Problem Book 3: Lecture Notes in Mathematics, 1573 8789 (1994) 


1994 
LOY RJ, WILLIS GA, 'THE APPROXIMATION PROPERTY AND NILPOTENT IDEALS IN AMENABLE BANACHALGEBRAS', BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 49 341346 (1994)



1994 
Gronbaek N, Johnson BE, Willis GA, 'AMENABILITY OF BANACH ALGEBRAS OF COMPACT OPERATORS', ISRAEL JOURNAL OF MATHEMATICS, 87 289324 (1994)



1994 
DALES HG, LOY RJ, WILLIS GA, 'HOMOMORPHISMS AND DERIVATIONS FROM B(E)', JOURNAL OF FUNCTIONAL ANALYSIS, 120 201219 (1994)



1994 
WILLIS G, 'THE STRUCTURE OF TOTALLY DISCONNECTED, LOCALLY COMPACTGROUPS', MATHEMATISCHE ANNALEN, 300 341363 (1994)



1993 
Somerset DWB, Willis GA, 'On the closure of the prime radical of a Banach algebra', Proceedings of the Edinburgh Mathematical Society (Series 2), 36 421425 (1993)



1993 
Grønbæk N, Willis GA, 'Approximate identities in Banach algebras of compact operators', Canadian Mathematical Bulletin, 36 4553 (1993) 


1992 
Willis G, 'The Continuity Of Derivations From Group Algebras: Factorizable And Connected Groups', Journal of the Australian Mathematical Society, 52 185204 (1992)
A group is said to be factorizable if it has a finite number of abelian subgroups, H1H2Hnsuch that G = H1H2HnIt is shown that, if G is a factorizable or connected locally compact ... [more]
A group is said to be factorizable if it has a finite number of abelian subgroups, H1H2Hnsuch that G = H1H2HnIt is shown that, if G is a factorizable or connected locally compact group, then every derivation from Cl(G) to an arbitrary C(G)bimodule X is continuous. © 1992, Australian Mathematical Society. All rights reserved.



1992 
Dixon PG, Willis GA, 'Approximate identities in extensions of topologically nilpotent Banach algebras', Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 122 4552 (1992) 


1992 
Willis GA, 'The compact approximation property does not imply the approximation property', Studia Mathematica, 99108 (1992) 


1992 
Willis G, 'Examples of factorization without bounded approximate units', Proceedings of the London Mathematical Society, s364 602624 (1992)
Examples are given of Banach algebras which do not have bounded approximate units but in which every element is a product. Another algebra is constructed in which there are elemen... [more]
Examples are given of Banach algebras which do not have bounded approximate units but in which every element is a product. Another algebra is constructed in which there are elements which are not products but every element is the sum of two products. Most of the examples are commutative and separable. These examples suggest that there may be a connection between factorization questions and the topology of the carrier space of a Banach algebra. © 1992 University of North Carolina Press.



1991 
MORAN W, WILLIS GA, 'BOUNDARIES AND MODULAR IDEALS ON LOCALLY COMPACTGROUPS', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 112 819827 (1991)



1990 
WILLIS GA, 'PROBABILITYMEASURES ON GROUPS AND SOME RELATED IDEALS IN GROUPALGEBRAS', JOURNAL OF FUNCTIONAL ANALYSIS, 92 202263 (1990)



1989 
LOY RJ, WILLIS GA, 'CONTINUITY OF DERIVATIONS ON B(E) FOR CERTAIN BANACH SPACESE', JOURNAL OF THE LONDON MATHEMATICAL SOCIETYSECOND SERIES, 40 327346 (1989)



1988 
WILLIS GA, 'CONTINUITY OF TRANSLATION INVARIANT LINEAR FUNCTIONALS ON C0(G) FOR CERTAIN LOCALLY COMPACT GROUPSG', MONATSHEFTE FUR MATHEMATIK, 105 161164 (1988)



1986 
WILLIS GA, 'THE CONTINUITY OF DERIVATIONS AND MODULE HOMOMORPHISMS', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES APURE MATHEMATICS AND STATISTICS, 40 299320 (1986)



1986 
WILLIS GA, 'TRANSLATION INVARIANT FUNCTIONALS ON LP(G) WHEN G IS NOT AMENABLE', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES APURE MATHEMATICS AND STATISTICS, 41 237250 (1986)



1983 
Willis GA, 'Factorization in codimension two ideals of group algebras', Proceedings of the American Mathematical Society, 89 95100 (1983)
Let G be a finitely generated group and I be a closed, twosided ideal with codimension two in L1(G). Then the linear span of the set of all products in is equal to I. © 1983 Amer... [more]
Let G be a finitely generated group and I be a closed, twosided ideal with codimension two in L1(G). Then the linear span of the set of all products in is equal to I. © 1983 American Mathematical Society.



1982 
Willis G, 'Factorization in codimension one ideals of group algebras', Proceedings of the American Mathematical Society, 86 599601 (1982)
It is shown that if G is a locally compact group and I is a closed, twosided ideal with codimension one in L1(G), then I2 = I. © 1982 American Mathematical Society.... [more]
It is shown that if G is a locally compact group and I is a closed, twosided ideal with codimension one in L1(G), then I2 = I. © 1982 American Mathematical Society.



1982 
Willis GA, 'Approximate Units in Finite Codimensional Ideals of Group Algebras', Journal of the London Mathematical Society, s226 143154 (1982)


