Associate Professor

# Associate Professor Ian Doust

Science
Sch of Mathematics & Statistic

BSc (WAust),  MSc (Toronto),  PhD (Edin),  FAustMS

Much of my work is in the area of operator theory and the geometry of Banach spaces. In particular my work has concentrated on the relationships between functional calculus and integral representations for operators, and how this is affected by geometric properties of the spaces on which the operators act. More recently I have been investigating geometric properties of metric spaces.

Phone
9385 7097
E-mail
Location
School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 The Red Centre Room 6113

## Publications

• Journal articles | 2021
Associate Professor Ian Doust
Al-shakarchi S; Doust I, 2021, 'AC(σ) spaces for polygonally inscribed curves', Banach Journal of Mathematical Analysis, vol. 15, http://dx.doi.org/10.1007/s43037-020-00110-w
Journal articles | 2021
Associate Professor Ian Doust
Doust I; Robertson G; Stoneham A; Weston A, 2021, 'Distance matrices of subsets of the Hamming cube', Indagationes Mathematicae, vol. 32, pp. 646 - 657, http://dx.doi.org/10.1016/j.indag.2021.01.004
Journal articles | 2020
Associate Professor Ian Doust
Al-shakarchi S; Doust I, 2020, 'Isomorphisms of $AC(σ)$ spaces for linear graphs', Advances in Operator Theory, http://dx.doi.org/10.1007/s43036-020-00053-x
Journal articles | 2019
Associate Professor Ian Doust
Blower G; Brett C; Doust I, 2019, 'Statistical mechanics of the periodic Benjamin-Ono equation', Journal of Mathematical Physics, vol. 60, pp. 093302 - 093302, http://dx.doi.org/10.1063/1.5091737
Journal articles | 2019
Associate Professor Ian Doust
Doust I, 2019, 'A note on positive $\mathcal{AN}$ operators', Bulletin of the Australian Mathematical Society, vol. 100, pp. 129 - 130, http://dx.doi.org/10.1017/S0004972718001296
Journal articles | 2017
Associate Professor Ian Doust
Doust I; Sánchez S; Weston A, 2017, 'Asymptotic negative type properties of finite ultrametric spaces', Journal of Mathematical Analysis and Applications, vol. 446, pp. 1776 - 1793, http://dx.doi.org/10.1016/j.jmaa.2016.09.069
Journal articles | 2017
Associate Professor Ian Doust
Blower G; Doust I, 2017, 'Operational calculus and integral transforms for groups with finite propagation speed', Advances in Pure and Applied Mathematics, vol. 8, pp. 265 - 283, http://dx.doi.org/10.1515/apam-2015-0049
Journal articles | 2016
Associate Professor Ian Doust
Blower G; Brett C; Doust I, 2016, 'Hill's spectral curves and the invariant measure of the periodic KdV equation', Bulletin des Sciences Mathematiques, vol. 140, pp. 864 - 899, http://dx.doi.org/10.1016/j.bulsci.2016.03.005
Journal articles | 2015
Associate Professor Ian Doust
Doust I; Leinert M, 2015, 'Isomorphisms of $AC(σ)$ spaces', Studia Mathematica, vol. 228, pp. 7 - 31, http://dx.doi.org/10.4064/sm228-1-3
Journal articles | 2014
Associate Professor Ian Doust
Blower G; Brett C; Doust I, 2014, 'Logarithmic Sobolev inequalities and spectral concentration for the cubic Schrödinger equation', Stochastics, vol. 86, pp. 870 - 881, http://dx.doi.org/10.1080/17442508.2014.882924
Journal articles | 2014
Associate Professor Ian Doust
Doust I; Sánchez S; Weston A, 2014, 'A direct proof that ℓ∞(3) has generalized roundness zero', Expositiones Mathematicae, vol. Available online 25 June 2014, pp. 259 - 267, http://dx.doi.org/10.1016/j.exmath.2014.06.001
Journal articles | 2013
Associate Professor Ian Doust
Doust I; Leinert M, 2013, 'Approximation in $AC(σ)$', ArXiv, https://www.researchgate.net/publication/259211398_Approximation_in_ACsigma
Journal articles | 2012
Associate Professor Ian Doust
Caffarelli E; Doust I; Weston A, 2012, 'Metric trees of generalized roundness one', Aequationes Mathematicae, vol. 83, pp. 239 - 256, http://dx.doi.org/10.1007/s00010-011-0108-8
Journal articles | 2011
Associate Professor Ian Doust
Doust IR; Ashton B, 2011, 'AC(σ) operators', Journal of Operator Theory, vol. 65, pp. 255 - 279
Journal articles | 2010
Associate Professor Ian Doust
Doust IR; Terauds V, 2010, 'Extensions of an AC(σ) functional calculus', Journal of Mathematical Analysis and Applications, vol. 362, pp. 100 - 106, http://dx.doi.org/10.1016/j.jmaa.2009.10.001
Journal articles | 2009
Associate Professor Ian Doust
Doust IR; Ashton B, 2009, 'Compact AC(σ) operators', Integral Equations and Operator Theory, vol. 63, pp. 459 - 472, http://dx.doi.org/10.1007/s00020-009-1667-0
Journal articles | 2008
Associate Professor Ian Doust
Doust I; Weston A, 2008, 'Corrigendum to "Enhanced negative type for finite metric trees" [J. Funct. Anal. 254 (2008) 2336-2364] (DOI:10.1016/j.jfa.2008.01.013)', Journal of Functional Analysis, vol. 255, pp. 532 - 533, http://dx.doi.org/10.1016/j.jfa.2008.03.018
Journal articles | 2008
Associate Professor Ian Doust
Doust IR; Weston A, 2008, 'Enhanced negative type for finite metric trees', Journal of Functional Analysis, vol. 254, pp. 2336 - 2364, http://dx.doi.org/10.1016/j.jfa.2008.01.013
Journal articles | 2008
Associate Professor Ian Doust
Doust IR; Lancien G, 2008, 'The spectral type of sums of operators on non-Hilbertian Banach lattices', Journal of the Australian Mathematical Society, vol. 84, pp. 193 - 198, http://dx.doi.org/10.1017/S1446788708000244
Journal articles | 2006
Associate Professor Ian Doust
Ashton B; Doust IR, 2006, 'A comparison of algebras of functions of bounded variation', Proceedings of the Edinburgh Mathematical Society, vol. 49, pp. 575 - 591, http://dx.doi.org/10.1017/S0013091504001130
Journal articles | 2005
Associate Professor Ian Doust
Blower G; Doust IR, 2005, 'A maximal theorem for holomorphic semigroups', Quarterly Journal of Mathematics, vol. 56, pp. 21 - 30, http://dx.doi.org/10.1093/qmath/hah024
Journal articles | 2005
Associate Professor Ian Doust
Ashton BC; Doust IR, 2005, 'Functions of bounded variation on compact subsets of the plane', Studia Mathematica, vol. 169, pp. 163 - 188, http://dx.doi.org/10.4064/sm169-2-5
Journal articles | 2005
Associate Professor Ian Doust
Doust IR; Gillespie TA, 2005, 'Schur multiplier projections on the Von Neumann-Schatten Classes', Journal of Operator Theory, vol. 53, pp. 251 - 272
Journal articles | 2005
Associate Professor Ian Doust
Doust I; Hirschhorn MD; Ho J, 2005, 'Trigonometric Identities, Linear Algebra, and Computer Algebra', The American Mathematical Monthly, vol. 112, pp. 155 - 164, http://dx.doi.org/10.1080/00029890.2005.11920179
Journal articles | 2005
Associate Professor Ian Doust
Doust IR; Hirschhorn MD; Ho J, 2005, 'Trigonometric identities, linear algebra, and computer algebra', American Mathematical Monthly, vol. 112, pp. 155 - 164, http://dx.doi.org/10.2307/30037413
Journal articles | 2003
Associate Professor Ian Doust
Doust IR; Gillespie TA, 2003, 'Well-boundedness of sums and products of operators', Journal of the London Mathematical Society - Second Series, vol. 68, pp. 183 - 192, http://dx.doi.org/10.1112/S0024610703004447
Journal articles | 2002
Associate Professor Ian Doust
Ashton BC; Cheng Q; Doust IR, 2002, 'Some remarks on well-bounded and scalar-type decomposable operators', Houston Journal of Mathematics, vol. 28, pp. 849 - 864
Journal articles | 2001
Associate Professor Ian Doust
Journal articles | 2001
Associate Professor Ian Doust
Cheng Q; Doust IR, 2001, 'Well-bounded operators on non-reflexive Banach spaces II', Quaestiones Mathematicae, vol. 24, pp. 183 - 191, http://dx.doi.org/10.1080/16073606.2001.9639206
Journal articles | 2001
Associate Professor Ian Doust
Qingping C; Doust I, 2001, 'Compact well-bounded operators', Glasgow Mathematical Journal, vol. 43, pp. 467 - 475, http://dx.doi.org/10.1017/s0017089501030087
Journal articles | 2000
Associate Professor Ian Doust
Doust IR; Gillespie TA, 2000, 'An example in the theory of AC-operators', Proceedings of the American Mathematical Society, vol. 129, pp. 1453 - 1457
Journal articles | 1997
Associate Professor Ian Doust
Berkson E; Doust IR; Gillespie TA, 1997, 'Properties of AC-operators', ACTA Scientiarum Mathematicarum, pp. 249 - 271
Journal articles | 1997
Associate Professor Ian Doust
Cheng Q; Doust IR, 1997, 'The dual theory of well-bounded operators', Journal of Operator Theory, pp. 35 - 50
Journal articles | 1996
Associate Professor Ian Doust
Cowling MG; Doust IR; Mcintosh A; Yagi A, 1996, 'Banach space operators with bounded H^{infinity} functional calculus', Journal of the Australian Mathematical Society Series A - Pure Mathematics and Statistics, vol. 60, pp. 51 - 89
Journal articles | 1996
Associate Professor Ian Doust
Cheng Q; Doust IR, 1996, 'Well-bounded operators on nonreflexive Banach spaces', Proceedings of the American Mathematical Society, vol. 124, pp. 799 - 808
Journal articles | 1996
Associate Professor Ian Doust
Doust IR; Walden BL, 1996, 'Compact AC-operators', Studia Mathematica, vol. 117, pp. 275 - 287
Journal articles | 1994
Associate Professor Ian Doust
Doust IR; deLaubenfels R, 1994, 'Functional Calculus, Integral Representations, and Banach Space Geometry', Quaestiones Mathematicae, vol. 17, pp. 161 - 171, http://dx.doi.org/10.1080/16073606.1994.9631755
Journal articles | 1994
Associate Professor Ian Doust
Doust I, 1994, 'A weaker condition for normality', Glasgow Mathematical Journal, vol. 36, pp. 249 - 253, http://dx.doi.org/10.1017/S0017089500030792
Journal articles | 1993
Associate Professor Ian Doust
DOUST I; BOZHOU Q, 1993, 'THE SPECTRAL THEOREM FOR WELL-BOUNDED OPERATORS', JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, vol. 54, pp. 334 - 351, http://dx.doi.org/10.1017/S1446788700031827
Journal articles | 1992
Associate Professor Ian Doust
Doust I; Ricker WJ, 1992, 'Spectral projections for Hermitian operators', Linear Algebra and Its Applications, vol. 175, pp. 75 - 96, http://dx.doi.org/10.1016/0024-3795(92)90303-R
Journal articles | 1992
Associate Professor Ian Doust
Doust IR, 1992, 'Interpolation and extrapolation of well-bounded operators', Journal of Operator Theory, vol. 28, pp. 229 - 250, http://www.theta.ro/
Journal articles | 1990
Associate Professor Ian Doust
Doust IR, 1990, 'A study of counting', Australian Universities' Review, pp. 18 - 19
Journal articles | 1990
Associate Professor Ian Doust
Doust IR, 1990, 'Staffing in Higher Education - Mathematics in the Nineties', Gazette of the Australian Mathematical Society, vol. 17, pp. 43 - 46
Journal articles | 1989
Associate Professor Ian Doust
Doust I, 1989, 'Well-bounded and scalar-type spectral operators on spaces not containing c0', Proceedings of the American Mathematical Society, vol. 105, pp. 367 - 370, http://dx.doi.org/10.1090/S0002-9939-1989-0939963-X
Journal articles | 1989
Associate Professor Ian Doust
Doust I, 1989, 'Well-Bounded And Scalar-Type Spectral Operators On lpSpaces', Journal of the London Mathematical Society, vol. s2-39, pp. 525 - 534, http://dx.doi.org/10.1112/jlms/s2-39.3.525
Journal articles |
Associate Professor Ian Doust
Al-shakarchi S; Doust I, 'Isomorphisms of $BV(σ)$ spaces', , http://arxiv.org/abs/2007.05701v2
Journal articles |
Associate Professor Ian Doust
Amini-Harandi A; Doust I; Robertson G, 'Roundness Properties of Banach spaces', , http://arxiv.org/abs/2105.13739v1
• Conference Papers | 2017
Associate Professor Ian Doust
Doust I; Al-shakarchi S, 2017, 'Isomorphisms of AC(σ) spaces for countable sets', in Böttcher A; Potts D; Stollmann P; Wenzel D (eds.), The Diversity and Beauty of Applied Operator Theory. Operator Theory: Advances and Applications, Springer International Publishing AG, part of Springer Nature, Chemnitz, pp. 193 - 206, presented at International Workshop on Operator Theory and its Applications (IWOTA), Chemnitz, 14 August 2017 - 18 August 2017, http://dx.doi.org/10.1007/978-3-319-75996-8_11
Conference Papers | 2010
Associate Professor Ian Doust
Blower G; Doust IR; Taggart RJ, 2010, 'A maximal theorem for holomorphic semigroups on vector-valued spaces', in Proceedings of the Centre for Mathematics and its applications, Centre for Mathematics and its Applications (CMA), Australian National University, Canberra, pp. 105 - 114, presented at Centre for Mathematics and its Applications (CMA), Australian National University, Canberra, 13 July 2009 - 17 July 2009
Conference Papers | 2007
Associate Professor Ian Doust
Doust IR; Lancien F; Lancien G, 2007, 'Spectral theory for linear operators on L¹ or C(K) spaces', in McIntosh A; Portal P (ed.), Proceedings of the Centre for Mathematics and its Applications, Australian National University, Australian National University, Canberra, pp. 1 - 10, presented at CMA/AMSI Research Symposium "Asymptotic Geometric Analysis, Harmonic Analysis, and Related Topics'', Murramarang, New South Wales, Australia, 21 February 2006 - 24 February 2006
Conference Papers | 2001
Associate Professor Ian Doust
Doust IR, 2001, 'Norms of 0-1 matrices in Cp', in Isaev A; Hassell A; McIntosh A; Sikora A (eds.), Proceedings of the Centre for Mathematics and its Applications, Australian National University, Australian National University, Canberra, pp. 50 - 55, presented at Geometric analysis and applications, Canberra, 26 June 2000 - 30 June 2000
Conference Papers | 1995
Associate Professor Ian Doust
Doust IR, 1995, 'Contractive projections on Lebesgue-Bochner spaces', in Jarosz K (ed.), Lecture Notes in Pure and Applied Mathematics, Dekker, New York, pp. 101 - 109, presented at Function spaces, Edwardsville, Illinois, 17 May 1994 - 20 May 1994
Conference Proceedings (Editor of) | 1991
Associate Professor Ian Doust
Doust I; Jefferies B, (ed.), 1991, 'Miniconference on Probability and Analysis', Austral. Nat. Univ., Canberra, Vol. 29, presented at Miniconference on Probability and Analysis, UNSW, 24 July 1991 - 26 July 1991
Conference Papers | 1989
Associate Professor Ian Doust
Doust IR, 1989, 'An example in the theory of spectral and well-bounded operators', in Doust I; Jefferies B; Li C; McIntosh A (eds.), An example in the theory of spectral and well-bounded operators, Austral. Nat. Univ., Canberra, pp. 83 - 90, presented at Miniconference on Operators in Analysis, 25 September 1989 - 27 September 1989
Conference Proceedings (Editor of) | 1989
Associate Professor Ian Doust
Doust I; Jefferies B; Li C; McIntosh A, (eds.), 1989, 'Miniconference on Operators in Analysis', Austral. Nat. Univ., Canberra, Vol. 24, presented at Miniconference on Operators in Analysis, Macquarie University, Sydney, 25 September 1989 - 27 September 1989
Conference Proceedings (Editor of) | 1989
Associate Professor Ian Doust
Doust IR; Jefferies BRF; Li C; McIntosh A, (eds.), 1989, 'Miniconference on Operators in Analysis. Proceedings of the miniconference held at Macquarie University, Sydney, September 25-27, 1989. Proceedings of the Centre for Mathematical Analysis, Australian National University, 24.', Australian National University, Centre for Mathematical Analysis, Canberra, Macquarie University, Sydney, Vol. 24, presented at Miniconference on Operators in Analysis, Macquarie University, Sydney, 25 September 1989 - 27 September 1989
Conference Papers | 1988
Associate Professor Ian Doust
Doust IR, 1988, 'Contractive projections on Banach spaces', in Fitzpatrick S; Giles J (ed.), Contractive projections on Banach spaces, Austral. Nat. Univ.,, Canberra, pp. 50 - 58, presented at Miniconference on Functional Analysis & Optimization, Canberra, 08 August 1988 - 24 August 1988