Tatjana (Tanja) Eisner

Professor, University of Leipzig

Postal address
Institute of Mathematics, University of Leipzig
P.O. Box 100 920, 04009 Leipzig, Germany
Visiting address Office A 427, Augustusplatz 10, 04109 Leipzig (map)
Phone (Fax) +49 341 97 32167   (+49 341 97 32187)
eisner @ math.uni-leipzig.de

Summer School "Analysis of multiple ergodic averages"
Summer School "Paradoxical decompositions, fractals and dynamics"

Research Interests - Curriculum Vitae - Books - Papers - Teaching - Links

Main Research Interests

  • functional analysis/ operator theory
  • dynamical systems/ ergodic theory

Curriculum Vitae


Tanja Eisner, Bálint Farkas, Ergodic Theorems, submitted.

Graduate Texts in Mathematics, Springer, 2015. 628 pp.
(Here you can find a draft version.)

Tanja Eisner
Operator Theory: Advances and Applications, Vol. 209.
Birkhäuser Verlag, Basel, 2010. 204 pp.
(Here you can find a draft version.)

Tanja Eisner, Birgit Jacob, André Ran, Hans Zwart (eds.)
Operator Theory: Advances and Applications, Birkhäuser Verlag, 2016.


  1. A view on multiple recurrence, Indag. Math. 34 (2023), 231-247. (Special issue on the occasion of Jaap Korevaar's 100-th birthday) [arXiv]
  2. (with Agnes Radl) Embeddability of real and positive operators, Linear Multilinear Algebra 70 (2022), 3747-3767. [arXiv]
  3. (with Zoltán Buczolich) Divergence of weighted square averages in L1, Adv. Math. 384 (2021), Paper No. 107727, 19 pp. [arXiv]
  4. (with Vladimir Müller) Power bounded operators and the mean ergodic theorem for subsequences, J. Math. Anal. Appl. 493 (2021), 124523, 25 pp. [arXiv]
  5. Nilsystems and ergodic averages along primes, Ergodic Theory Dynam. Systems 40 (2020), 2769-2777. [arXiv]
  6. (with Guy Cohen, Christophe Cuny and Michael Lin) Resolvent conditions and growth of powers of operators, J. Math. Anal. Appl. 487 (2020), 124035, 24 pp. [arXiv]
  7. (with Bálint Farkas and Christophe Cuny) Wiener's lemma along primes and other subsequences, Adv. Math. 347 (2019), 340-383. [arXiv]
  8. (with Jakub Konieczny) Automatic sequences as good weights for ergodic theorems, Discrete Contin. Dyn. Syst. 38 (2018), no. 8, 4087-4115. [arXiv]
  9. (with Michael Lin) On modulated ergodic theorems, J. Nonlinear Var. Anal. 2 (2018), 131-154. (special issue dedicated to Simeon Reich). [arXiv]
  10. (with Dávid Kunszenti-Kovács) On the pointwise entangled ergodic theorem, J. Math. Anal. Appl. 449 (2017), 1754-1769. [arXiv]
  11. (with Ben Krause) (Uniform) convergence of twisted ergodic averages, Ergodic Theory Dynam. Systems 36 (2016), 2172-2202. [arXiv]
  12. A polynomial version of Sarnak's conjecture, C. R. Math. Acad. Sci. Paris 353 (2015), 569-572. [arXiv]
  13. Linear sequences and weighted ergodic theorems, Abstr. Appl. Anal. 2013, Art. ID 815726. [arXiv]
  14. (with Tamás Mátrai) On typical properties of Hilbert space operators, Israel J. Math. 195 (2013), 247-281. [arXiv]
  15. (with Pavel Zorin-Kranich) Uniformity in the Wiener-Wintner theorem for nilsequences, Discrete Contin. Dyn. Syst. 33 (2013) 3497-3516. [arXiv]
  16. (with Dávid Kunszenti-Kovács) On the entangled ergodic theorem, Ann. Scuola Norm. Sup. Pisa Cl. Sci. XII (2013), 141-156. [arXiv]
  17. (with Terence Tao) Large values of the Gowers-Host-Kra seminorms, J. Anal. Math. 117 (2012), 133-186. [arXiv]
  18. (with Sophie Grivaux) Hilbertian Jamison sequences and rigid dynamical systems, J. Funct. Anal. 261 (2011), 2013-2052. [arXiv]
  19. (with Tim Austin and Terence Tao) Nonconventional ergodic averages and multiple recurrence for von Neumann dynamical systems, Pacific J. Math. 250 (2011), 1-60. [arXiv]
  20. A "typical" contraction is unitary, Enseign. Math. (2) 56 (2010), 403-410. [arXiv]
  21. (with András Serény) On the weak analogue of the Trotter-Kato theorem, Taiwanese J. Math. 14 (2010), 1411-1416. [arXiv]
  22. Embedding operators into strongly continuous semigroups, Arch. Math. (Basel) 92 (2009), 451-460. [arXiv]
  23. (with András Serény) Category theorems for stable semigroups, Ergodic Theory Dynamical Systems 29 (2009), 487-494. [arXiv]
  24. (with Hans Zwart) The growth of a C0-semigroup characterised by its cogenerator, J. Evol. Equ. 8 (2008), 749-764. [arXiv]
  25. (with András Serény) Category theorems for stable operators on Hilbert spaces, Acta Sci. Math. (Szeged) 74 (2008), 259-270. [arXiv]
  26. (with András Bátkai and Yuri Latushkin) The spectral mapping property of delay semigroups, Compl. Anal. Oper. Theory 2 (2008), 273-283. [pdf-file]
  27. (with Hans Zwart) A note on polynomially growing C0-semigroups, Semigroup Forum 75 (2007), 438-445. [pdf-file]
  28. (with Bálint Farkas, Rainer Nagel and András Serény) Weakly and almost weakly stable C0-semigroups, Int. J. Dyn. Syst. Differ. Equ. 1 (2007), 44-57. [arXiv]
  29. (with Hans Zwart) Continuous-time Kreiss resolvent condition on infinite-dimensional spaces, Math. Comp. 75 (2006), 1971-1985. [pdf-file]
  30. Polynomially bounded semigroups, Semigroup Forum 70 (2005), 118-126. [pdf-file], [erratum]
  31. (with Olga M. Katkova and Anna M. Vishnyakova) On entire functions having Taylor sections with only real zeros, Mat. Fiz. Anal. Geom. 11 (2004), 449-469.
  32. (with Olga M. Katkova and Anna M. Vishnyakova) On power series having sections with only real zeros, Comput. Methods Funct. Theory 3 (2003), 425-441.
  33. On variation preserving operators, Mat. Fiz. Anal. Geom. 10 (2003), 94-105.

Papers in proceedings

  1. (with Rainer Nagel) Arithmetic progressions - an operator theoretic view, Discrete Contin. Dyn. Syst. Series S, 6 (2013), 657-667.
  2. (with Bálint Farkas) Weak stability of orbits of C0-semigroups on Banach spaces. In H. Amann, W. Arendt, M. Hieber, F. Neubrander, S. Nicaise, J. von Below (eds), Functional Analysis and Evolution Equations. The Günter Lumer Volume (2007), 201-208. [pdf-file]


  • Rigidity of contractions on Hilbert spaces. [arXiv]

Some Teaching


Study/career advice from Anton Deitmar and Terence Tao
n-City-Seminar     "Dynamics and Geometry" Seminar     Functional Analysis Group
Journal for Analysis and Its Applications     Max Planck Institute for Math. in the Sciences
Miniworkshops on Operator Theoretic Aspects of Ergodic Theory ( Leipzig, Kiel, Wuppertal, Tübingen, Feldkirch, Leipzig, Wuppertal, Kiel)
MathSciNet     ArXiv     Trains in Germany     Functional analysis group Tübingen     Colloquium in Honour of Thomas Kühn