Univ.-Prof. Dr. Eva Kopecká

Univ.-Prof. Dr. Eva Kopecká

| +43 512 507 53940

| Eva.Kopecka@uibk.ac.at

| Technikerstraße 13, 7.OG, Zi.-Nr.: 725, A-6020 Innsbruck

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Research interests:

Main research fields: Functional Analysis, Geometry of Banach Spaces, Nonlinear Analysis.
Main keywords: reflexivity, convexity, measure, iteration of projections, greedy algorithm

Teaching

Lehrveranstaltungen im SoSe 2024

  • Diskrete Mathematik, VO 3
    Di 12.45 - 13.30 Uhr, HS G, Mi 15.30 - 17.00 Uhr, HS  10
  • Diskrete Mathematik, PS 2
    Di 13.45 - 15.15 Uhr, HS G
  • Einführung in die höhere Analysis (gemeinsam mit Birgit Schörkhuber), VO 2 
    Di 08.30 - 10.00 Uhr, HS D
  • Forschungsseminar: Funktionalanalysis, SE 2
    Di 17.15 - 18.45 Uhr, HS D

Education:

  • 2000    Habilitation in Mathematics, Kepler University, Linz, Austria
  • 1995    Ph.D. in Mathematics, Charles University, Prague, Czech Republic
  • 1990    RNDr. in Mathematics, Charles University, Prague, Czech Republic

Positions:

10.2012 - present   Department of Mathematics, University of Innsbruck, Austria
Professor

08.2017 - 12.2017   MSRI, Berkeley, CA, USA.
Research Member

08.2011 - 12.2011   MSRI, Berkeley, CA, USA.
Research Professor

01.2004 - 09.2012   Department of Mathematics, Kepler University in Linz, Austria
Dozent

03.2003 - 09.2003   Department of Mathematics, Kepler University in Linz, Austria.
Visiting Professor

01.2002 - 06. 2002   Department of Mathematics, University of South Carolina, Columbia, SC, USA.
Research Associate

01.2001 - 06. 2001   Department of Mathematics, University of South Carolina, Columbia, SC, USA.
Research Associate

06.1995 - 09.2012   Institute of Mathematics, Czech Academy of Sciences, Prague, Czech Republic.
Researcher
 

Publications:

  • E. Kopecká, L. Zajíček, The Fréchet derivative is in the first Baire class, arXiv:2608.02233
  • P. A. Borodin, E. Kopecká, Consecutive Projections and Greedy Approximation in Hilbert Space, Journal of Mathematical Sciences, Vol. 299, No. 3 (2026), 314–343. MR5069854
  • P.A. Borodin, E. Kopecká, Convergence of remote projections onto convex sets, Pure Appl. Funct. Anal. 8 (2023), 1603-1620. MR4686570
  • P.A. Borodin, E. Kopecká, Weak limits of consecutive projections or greedy steps, Proc. Steklov Inst. Math. 319 (2022), 56-63. MR4563384.
  • P.A. Borodin, E. Kopecká, Sequences of m-term deviations in Hilbert space, to appear in J. of Approximation Theory.
  • P.A. Borodin, E. Kopecká, Alternating projections, remotest projections, and greedy approximation, J. of Approximation Theory 260 (2020), 105486.
  • E. Kopecká, When products of projections diverge, J. London Math. Soc. (2) 102 (2020), 345-367.
  • M. Dymond, V. Kaluža, E. Kopecká, Mapping n grid points onto a square forces an arbitrary large Lipschitz constant, Geom. Funct. Anal. Vol. 28 (2018), 589-644.
  • E. Kopecká, A. Paszkiewicz: Strange products of projections, Israel J. Math. 219 (2017), 271–286. (arxiv)
  • E. Kopecká, V. Müller: A product of three projections. Studia Math. 223 (2014), 175-186. doi:10.4064/sm223-2-4
  • E. Kopecká, S. Reich, Approximating fixed points in the Hilbert ball, J. Nonlinear Convex Anal. 15 (2014), 819–829 (link)
  • E. Kopecká, S. Reich, A note on alternating projections in Hilbert space, J. Fixed Point Theory Appl. 12 (2012), 41–47. doi:10.1007/s11784-013-0097-4
  • E. Kopecká, Bootstrapping Kirszbraun's extension theorem, Fund. Math. 217 (2012), 13–19. doi:10.4064/fm217-1-2
  • E. Kopecká, Extending Lipschitz mappings continuously, J. Applied Anal. 18 (2012), 167–177. doi:10.1515/jaa-2012-0011
  • E. Kopecká, D. Reem, S. Reich, Zone diagrams in compact subsets of uniformly convex normed spaces, Israel J. Math. 188 (2012), 1–23 doi:10.1007/s11856-011-0094-5 (arxiv).
  • E. Kopecká, S. Reich, Continuous extension operators and convexity, Nonlinear Anal. 74 (2011), 6907–6910. doi:10.1016/j.na.2011.07.013
  • E. Kopecká, S. Reich, Alternating projections and orthogonal decompositions, J. Nonlinear Convex Anal. 12 (2011), 155–159. (link)
  • E. Kopecká, S. Reich, Another note on the von Neumann alternating projections algorithm, J. Nonlinear Convex Anal. 11 (2010), 455–460. (link)
  • E. Kopecká, D. Reem, S. Reich, Existence of zone diagrams in compact subsets of uniformly convex spaces, CCCG 2010, University of Manitoba, 17–20. (link)
  • E. Kopecká, S. Reich, A mean ergodic theorem for nonlinear semigroups on the Hilbert ball, J. Nonlinear Convex Anal. 11 (2010), 185–197. (link)
  • B. Kirchheim, E. Kopecká, S. Müller, Monotone curves, Math. Ann. 351 (2011), 81–94. doi: 10.1007/s00208-010-0594-3
  • E. Kopecká, S. Reich, Asymptotic behavior of resolvents of coaccretive operators in the Hilbert ball, Nonlinear Anal. 70 (2009), 3187–3194. doi:10.1016/j.na.2008.04.023
  • B. Kirchheim, E. Kopecká, S. Müller, Do projections stay close together?, J. Math. Anal. Appl. 350 (2009), 859–871. doi:10.1016/j.jmaa.2008.09.039
  • E. Kopecká, S. Reich, A note on the approximation of fixed points in the Hilbert ball, J. Nonlinear Convex Anal. 9 (2008), 361–367. (link)
  • E. Kopecká, Spokes, mirrors and alternating projections, Nonlinear Anal. 68 (2008), 1759–1764. doi:10.1016/j.na.2007.01.006
  • E. Kopecká, S. Reich, Nonexpansive retracts in Banach spaces, Banach Center Publications 77 (2007), 161–174. doi: 10.4064/bc77-0-12
  • E. Kopecká, Small set in a large box, Math Notes (Mat. Zametki) 81 (2007), 308-317.  See also Real Analysis Exchange, Summer Symposium 2007, 135–140.doi: 10.1134/S0001434607030054
  • E. Kopecká, S. Reich, Hyperbolic monotonicity in the Hilbert ball, Fixed Point Theory Appl. 2006 (5) (2006), 1–15. doi: 10.1155/FPTA/2006/78104
  • E. Kopecká, Almost isometries and orthogonality, J. Funct. Anal. 222 (2005), 253–273. doi: 10.1016/j.jfa.2005.01.006
  • E. Kopecká, S. Reich, A note on the von Neumann alternating projections algorithm, J. Nonlinear Convex Anal. 5 (2004), 379–386. MR 2006d:90230.
  • E. Matoušková, S. Reich, A.J. Zaslavski, Genericity in nonexpansive mapping theory, in: Advanced Courses of Mathematical Analysis, Vol. I, (A. Aizpuru Tomás and F. Léon Saavedra, Editors), World Scientific, 2004, pp. 81–98. MR 2006d:47091.
  • H.H. Bauschke, E. Matoušková, S. Reich, Projection and proximal point methods: convergence results and counterexamples, Nonlinear Anal. 56 (2004), 715–738. MR 2004m:47116.
  • E. Matoušková, S. Reich, The Hundal example revisited, J. Nonlinear Convex Anal. 4 (2003), 411–427. MR 2005a:47096.
  • E. Matoušková, S. Reich, Reflexivity and approximate fixed points, Studia Math. 159 (2003), 403–415. MR 2005a:46020.
  • E. Matoušková, M. Zelený, A note on intersections of non-Haar null sets, Colloq. Math. 96 (2003), 1–4. MR 2004h:28001.
  • E. Matoušková, Bilipschitz mappings of nets, Real Anal. Exchange 29 (2003), 89–106. MR 2004g:46025.
  • E. Matoušková, Almost isometries of balls, J. Funct. Anal. 190 (2002), 507-525. MR 2003b:46018.
  • E. Matoušková, Translating finite sets into convex sets, Bull. London Math. Soc. 33 (2001), 711–714. MR 2002f:46019.
  • E. Matoušková, C. Stegall, Compact spaces with a finer metric topology and Banach spaces, in: T. Banakh (ed.), General Topology in Banach Spaces, Nova Sci. Publ., Huntington, NY, 2001, 81–101. MR 2003e:46029.
  • J. Lindenstrauss, E. Matoušková, D. Preiss, Lipschitz image of a measure-null set can have a null complement, Israel J. Math. 118 (2000), 207–219. MR 2001d:46032.
  • E. Matoušková, Lipschitz images of Haar null sets, Bull. London Math. Soc. 32 (2000), 235–244. MR 2001a:46013.
  • E. Matoušková, Extensions of continuous and Lipschitz functions, Canad. Math. Bull. 43 (2000), 208–217. MR 2001c:54009.
  • E. Matoušková, An almost nowhere Fréchet smooth norm on superreflexive spaces, Studia Math. 133 (1999), 93–99. MR 99m:46037.
  • J. Matoušek, E. Matoušková, A highly non-smooth norm on Hilbert space, Israel J. Math. 112 (1999), 1–27. MR 2001f:46065.
  • E. Matoušková, L. Zajíček, Second order differentiability and Lipschitz smooth points of convex functionals, Czechoslovak Math. Journ. 48 (123) (1998), 617–640. MR 99m:46107.
  • M. Fabian, M. Heisler, E. Matoušková, Remarks on continuous images of RN compacta, Comment. Math. Univ. Carolinae 39 (1998), 59–69. MR 99g:46014.
  • E. Matoušková, The Banach-Saks property and Haar null sets, Comment. Math. Univ. Carolinae 39 (1998), 71–80. MR 99g:46013.
  • E. Matoušková, Convexity and Haar null sets, Proc. Amer. Math. Soc. 125 (1997), 1793–1799. MR 97g:46008.
  • E. Matoušková, C. Stegall, A characterization of reflexive Banach spaces, Proc. Amer. Math. Soc. 124 (1996), 1083–1090. MR 96g:46005.
  • E. Matoušková, Concerning weak∗-extreme points, Comment. Math. Univ. Carolinae 36 (1995), 245–248. MR 96i:46014.
  • 3. E. Matoušková, One counterexample concerning the Fréchet differentiability of convex functions on closed sets, Acta Univ. Carolin., Math. and Phys. 34 (1993), 97–105. MR 95i:46055.
  • E. Matoušková, How small are the sets where the metric projection fails to be continuous, Acta Univ. Carolin., Math. and Phys. 33 (1992), 99–108. MR 96a:46029.
  • E. Kopecká, J. Malý, Remarks on delta-convex functions, Comment. Math. Univ. Carolinae 31 (1990), 501–510. MR 91k:26011.

 

Master Thesis: Deltaconvex Functions, 1990.

Ph. D. Thesis: Differentiation in Banach Spaces, 1995.

Habilitation Thesis: Lipschitz Mappings and Measure-Null Sets, 2000.

Selected additional research achievements

Organisation of conferences, scientific committees

For example: Connections for Women in Geometry and Probability in High Dimensions (MSRI, Berkeley, CA), 2017; between 1993 and 2024 co-organizer of 11 editions of the Analysis Seminar Research Workshop; Frontiers of Operator Theory (CIRM Marseille, France), 2021, member of the scientific committee; Functional Analysis in Lille, a conference in honor of Gilles Godefroy (Lille, France), 2022, member of the scientific committee; member of the meetings committee of European Mathematical Society, 2025-2028.

Grants

1994-96 GAčR 201/94/0069, Cooperating Investigator.
1997-99 GAAV A1019705, Principal Investigator
2001 DEPSCOR-ONR N00014-99-1-0547, Cooperating Investigator
2002 Prize of the Union of Czech Mathematicians and Physicists
2001-03 GAAV A1019103, Principal Investigator,
2003 Wichterle Prize of the Czech Academy of Sciences
2004-06 FWF P16674-N12, Principal Investigator
2006-08 GAčR 201/06/0018, Cooperating Investigator
2007-10 FWF P19643-N18, Principal Investigator
2009-11 IAA 100190901, Cooperating Investigator
2011-16 FWF P23628-N18, Principal Investigator
2012 GAčR 201/12/0290, Cooperating Investigator
2017 NSF 1440140, Cooperating Investigator,
2020-21 Moscow Center of Pure and Applied Mathematics, Cooperating Investigator
2021 HIM, Hausdorff Trimester Program, Fellowship

Theses Supervision served as an advisor of 39 bachelor, master, and doctoral theses.

Projects

Former Projects

  • Lipschitz Mappings and Homeomorphisms (FWF P16674-N12)
  • Lipschitz Mappings and Homeomorphisms (FWF P19643-N18)
  • Contractions: Extensions, Isometries, and Projections (FWF P23628-N18)
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