Faculty of Science and Technology

Yost, David (A/Prof) - Research

Current research projects/students

Lower bound theorems for general polytopes

Publications/conferences

Research articles

  1. (with A.G. Robertson) Chebyshev subspaces of operator algebras, J. London Math. Soc. 19 (1979) 523-531. MR0540068 (80j:46097), Zbl 396.46052.
  2. Best approximation and intersections of balls in Banach spaces, Bull. Austral. Math.Soc. 20 (1979) 285-300. MR0557239 (80m:46019), Zbl 407.41015.
  3. M-ideals, the strong 2-ball property and some renorming theorems, Proc. Amer. Math. Soc. 81 (1981) 299-303. MR0593475 (82f:46019), Zbl 471.46009.
  4. The n-ball properties in real and complex Banach spaces, Math. Scand. 50 (1982) 100-110. MR0664511 (83h:46030), Zbl 471.46010.
  5. Average distances in compact connected spaces, Bull. Austral. Math. Soc. 26 (1982) 331-342. MR0689406 (84e:52016), Zbl 485.54012.
  6. Intersecting balls in spaces of vector-valued functions, Lecture Notes in Math. 991 (1983) 296-302. MR0714193 (85m:46035)= Zbl 518.46011.
  7. A base norm space whose cone is not 1-generating, Glasgow Math. J. 25 (1984) 35-36. MR0731479 (85b:46029), Zbl 544.46014.
  8. Semi-M-ideals in complex Banach spaces, Rev. Roumaine Math. Pures Appl. 29 (1984) 619-623. MR0759522 (85i:46027), Zbl 578.46015.
  9. (with J.M. Borwein) Absolute norms on vector lattices, Proc. Edinburgh Math. Soc. 27 (1984) 215-222. MR0760617 (86a:46006), Zbl 589.46005.
  10. Best approximation operators in functional analysis, Proc. Centre Math. Anal. Austral. Nat. Univ. 8 (1984) 249-270. MR0799234 (87f:41063), Zbl 578.41039.
  11. (with K.F. Ng) Quasi-regularity in optimization, J. Austral. Math. Soc. Ser. A 41 (1986) 188-192. MR0848032 (88g:49024), Zbl 601.49014.
  12. (with B. Sims) Banach spaces with many projections, Proc. Centre Math. Anal. Austral. Nat. Univ. 14 (1986) 335-342. MR0912949 (89a:46042), Zbl 642.46020.
  13. Approximation by compact operators between C(X) spaces, J. Approx. Theory 49 (1987) 99-109. MR0874946 (88a:46025), Zbl 621.41025.
  14. There can be no Lipschitz version of Michael's selection theorem, North-Holland Mathematics Studies 150 (1988) 295-299. MR0930904 (89d:54012), Zbl3646.54021.
  15. (with P. Nickolas) The average distance property for subsets of euclidean space, Arch. Math. 50 (1988) 380-384. MR0937343 (89d:51026), Zbl 627.54013.
  16. Banach spaces isomorphic to proper M-ideals, Colloq. Math. 56 (1988) 99-106. MR0980515 (90b:46043), Zbl 698.46013.
  17. (with R. Pay´a) The two-ball property: transitivity and examples, Mathematika 35 (1988) 190-197. MR0986628 (90a:46036), Zbl 651.46024.
  18. (with ?A. Lima) Absolutely Chebyshev subspaces, Proc. Centre Math. Anal. Austral.Nat. Univ. 20 (1988) 116-127. MR1009599(90h:46030), Zbl 673.41035.
  19. (with B. Sims) Linear Hahn-Banach extension operators, Proc. Edinburgh Math. Soc. 32 (1989) 53-57. MR0981992 (90b:46042), Zbl 648.46004.
  20. (with K. Przes lawski) Continuity properties of selectors and Michael's theorem, Michigan Math. J. 36 (1989) 113-134. MR0989940 (90d:49010), Zbl 703.47041.
  21. (with J.F. Mena, R. Pay´a and A. Rodr´?guez) Absolutely proximinal subspaces of Banach spaces, J. Approx. Theory 65 (1991) 46-72. MR1098831 (92e:46037), Zbl 725.41031.
  22. Irreducible convex sets, Mathematika 38 (1991) 134-155. MR1116691 (92h:52006), Zbl 761.52011.
  23. (with K. Przes lawski) Lipschitz retracts, selectors and extensions, Michigan Math. J. 42 (1995) 555-571. MR1357625 (97g:54034), Zbl 920.54019.
  24. (with C. Ben´?tez and K. Przes lawski) A universal modulus for normed spaces, Studia Math., 127 (1998) 21-46. MR1488142 (99i:46005), Zbl 909.46008.
  25. (with A.M. Plichko) Complemented and uncomplemented subspaces of Banach spaces, Extracta Math. 15 (2000) 335-371. MR1823896 (2002j:46023), Zbl 981.46022.
  26. (with A.M. Plichko) The Radon-Nikod´ym Property does not imply the Separable Complementation Property, J. Funct. Anal. 180 (2001), 481-487. MR1814996 (2001m:46025), Zbl 992.46014.
  27. (with J.M.F. Castillo, M. Gonz´alez and A.M. Plichko) Twisted properties of Banach spaces, Math. Scand. 89 (2001), 217-244. MR1868175 (2002m:46014), Zbl 1026.46008.
  28. (with J. Tabor) Applications of Inverse limits to extensions of operators and approximation of Lipschitz functions, J. Approx. Theory, 116 (2002), 257-267. MR1911082 (2003j:41032), Zbl 1008.41018.
  29. (with F. Cabello S´anchez, J.M.F. Castillo & N. J. Kalton) Twisted sums with C(K) spaces, Trans. Amer. Math. Soc., 355 (2003), 4523-4541. MR1990760 (2004f:46010), Zbl 1066.46006.
  30. (with F. Cabello S´anchez, J.M.F. Castillo & Y. Moreno) Extension of L1-valued operators under a twisted light, Functional analysis and its applications, 59-70, North-Holland Math. Stud., 197, Elsevier, Amsterdam, 2004. MR2098870 (2005k:46029), Zbl 1097.46011.
  31. (with H.M. Jebreen & F.B.H. Jamjoom) Colocality and twisted sums of Banach spaces, J. Math. Anal. Appl. 323 (2006), 864-875. MR2260149 (2007k:46019), Zbl 1112.46014.
  32. Some indecomposable polyhedra, Optimization 56 (2007), no. 5-6, 715-724. MR2362716 (2008i:52015), Zbl 1165.52012.
  33. (with K. Przes lawski) Decomposability of polytopes, Disc. Comp. Geom., 39 (2008), no. 1-3, 460-468. MR2383771 (2008m:52028), Zbl 1141.52015.
  34. A different Johnson-Lindenstrauss space, New Zealand J. Math. 37 (2008), 47-49. MR2406564 (2009b:46042) = Zbl 1193.46011.
  35. Uniformly non-hexagonal Banach spaces, in: S. Dhompongsa, K. Goebel, W.A. Kirk, S. Plubtieng, B. Sims and S. Suanthai (editors), Proceedings of ICFPTA2007, the eighth International Conference on Fixed Point Theory and its Applications, Chiang Mai, Thailand, 16-22 July 2007, pages 211-217. Yokohama, Yokahama Publishers, 2008. ISBN 978-4-946552-31-1. MR2581796 (2011c:46036), Zbl 1188.46009.

Pedagogical and survey papers

  1. Space-filling curves and universal normed spaces, Ann. Univ. Sci. Budapest E¨otv¨os Sect. Math. 27 (1985) 33-36. MR0823087 (87h:54025), Zbl 603.46025.
  2. (with J. Cleary and S.A. Morris) Numerical geometry - numbers for shapes, Amer. Math. Monthly 93 (1986) 260-275. MR0835294 (87h:51043), Zbl 598.51014.
  3. If every doughnut is a teacup, then every Banach space is a Hilbert space, Notas de Matematica 1 (1987) 125-148. MR1119596 (92g:46010), Zbl 693.46011.
  4. L1 contains every two-dimensional normed space, Ann. Polon. Math. 49 (1988) 17-19. MR0985361 (90b:46047), Zbl 679.46016.
  5. Asplund spaces for beginners, Acta. Univ. Carolinae Math. Phys. 34 (1993) 159-177. MR1282979 (95h:46026), Zbl 815.46022.
  6. The Johnson-Lindenstrauss space, Extracta Math. 12 (1997) 185-192. MR1607165 (99a:46027), Zbl 906.46016.
  7. (with J.M.F. Castillo and F. Cabello S´anchez) Sobczyk's Theorem from A to B, Extracta Math. 15 (2000) 391-420. MR1823898 (2002a:46003), Zbl 981.46022.
  8. Integration: Reversing traditional pedagogy, Australian Senior Mathematics Journal 22 (2008), No. 2, 37-40.
  9. Lipschitz selections for multifunctions, in: Lai-Jiu Lin et al. (editors), Proceedings of ICFPTA2009, the ninth International Conference on Fixed Point Theory and its Applications, Chang Hua, Taiwan, 16-22 July 2009, pages 199-212. Yokohama, Yokahama Publishers, 2010. MR2762187 (2012g:54001), Zbl 1223.54025
  10. Quasilinear mappings, M-ideals and polyhedra, Operators and Matrices 6, no. 2, (2012), 279-286. MR2976118, Zbl 1263.46004

Professional memberships and associations

  • Council Member, Australian Mathematical Society

Research interests

  • Combinatorial Geometry
  • Convexity
  • Functional Analysis