• Lajos Molnár, full professor and head of department, University of Szeged, TTIK (leader of the research group)
  • Marcell Gaál, PhD student, University of Szeged, TTIK
  • Gergő Nagy, assistant professor, University of Debrecen, TTK
  • Miklós Pálfia, research fellow, Hungarian Academy of Sciences, TKI
  • Dániel Virosztek, assistant research fellow, Budapest University of Technology and Economics, TTK

Former members:

  • György Pál Gehér, postdoctoral research assistant, University of Reading, Faculty of Science
  • Eszter Novák-Gselmann, senior assistant professor, University of Debrecen, TTK
  • Patrícia Szokol, senior assistant professor, University of Debrecen, IK



List of publications of the research group:


  1. R. Beneduci and L. Molnár, On the standard K-loop structure of positive invertible elements in a C*-algebra, J. Math. Anal. Appl. 420 (2014), 551-562. (pdf)
  2. F. Botelho, J. Jamison and L. Molnár, Algebraic reflexivity of isometry groups and automorphism groups of some operator structures, J. Math. Anal. Appl. 408 (2013), 177-195. (pdf)
  3. F. Botelho, J. Jamison and L. Molnár, Surjective isometries on Grassmann spaces, J. Funct. Anal. 265 (2013), 2226-2238. (pdf)
  4. F. Botelho, L. Molnár and G. Nagy, Linear bijections on von Neumann factors commuting with λ-Aluthge transform, Bull. Lond. Math. Soc. 48 (2016), 74-84. (pdf)
  5. H.-Y. Chen, Gy. P. Gehér, C.-N. Liu, L. Molnár, D. Virosztek and N.-C. Wong, Generalized isometries of the positive definite cone with respect to the quantum χα2-divergence, Lett. Math. Phys., to appear. (pdf)
  6. G. Dolinar, B. Kuzma, G. Nagy and P. Szokol, Restricted skew-morphisms on matrix algebras, Linear Algebra Appl. 490 (2016), 1-17. (pdf)
  7. A. Efimov, M. Gaál and Sz.Gy. Révész, On integral estimates of non-negative positive definite functions, Bull. Aust. Math. Soc. 96 (2017), 117-125. (pdf)
  8. M. Gaál, Maps preserving a new version of quantum f-divergence, Banach J. Math. Anal., to appear. (pdf)
  9. M. Gaál, On certain generalized isometries of the special orthogonal group, submitted.
  10. M. Gaál and L. Molnár, Transformations on density operators and on positive definite operators preserving the quantum Rényi divergence, Period. Math. Hung. 74 (2017), 88-107. (pdf)
  11. M. Gaál and G. Nagy, Maps on positive operators preserving Rényi type relative entropies and maximal f-divergences, submitted.
  12. Gy. P. Gehér, An elementary proof for the non-bijective version of Wigner's theorem, Phys. Lett. A 378 (2014), 2054-2057. (pdf)
  13. Gy. P. Gehér, Asymptotic behaviour of Hilbert space operators with applications, PhD dissertation (2014). (pdf)
  14. Gy. P. Gehér, Characterization of Cesaro- and L-asymptotic limits of matrices, Linear Multilinear Algebra 63 (2015), 788-805. (pdf)
  15. Gy. P. Gehér, Maps on real Hilbert spaces preserving the area of parallelograms and a preserver problem on self-adjoint operators, J. Math. Anal. Appl. 422 (2015), 1402-1413. (pdf)
  16. Gy. P. Gehér, A contribution to the Aleksandrov conservative distance problem in two dimensions, Linear Algebra Appl., 481 (2015), 280-287. (pdf)
  17. Gy. P. Gehér, Asymptotic limits of operators similar to normal operators, Proc. Amer. Math. Soc. 143 (2015), 4823-4834. (pdf)
  18. Gy. P. Gehér, Is it possible to determine a point lying in a simplex if we know the distances from the vertices?, J. Math. Anal. Appl. 439 (2016), 651-663. (pdf)
  19. Gy. P. Gehér, Asymptotic behaviour and cyclic properties of weighted shifts on directed trees, J. Math. Anal. Appl. 440 (2016), 14-32. (pdf)
  20. Gy. P. Gehér, Bilateral weighted shift operators similar to normal operators, Oper. Matrices 10 (2016), 419-423. (pdf)
  21. Gy. P. Gehér, Wigner's theorem on Grassmann spaces, J. Funct. Anal. 273 (2017), 2994-3001. (pdf)
  22. Gy. P. Gehér, Surjective Kuiper isometries, Houston J. Math., to appear. (pdf)
  23. Gy. P. Gehér, On n-norm preservers and the Aleksandrov conservative n-distance problem, Aequationes Math., to appear. (pdf)
  24. Gy. P. Gehér, Symmetries of projective spaces and spheres, submitted.
  25. Gy. P. Gehér and G. Nagy, Maps on classes of Hilbert space operators preserving measure of commutativity, Linear Algebra Appl. 463 (2014), 205-227. (pdf)
  26. Gy. P. Gehér and P. Šemrl, Isometries of Grassmann spaces, J. Funct. Anal. 270 (2016), 1585-1601. (pdf)
  27. Gy. P. Gehér and T. Titkos, A characterisation of isometries with respect to the Lévy-Prokhorov metric, Ann. Sc. Norm. Super. Pisa Cl. Sci., to appear. (pdf)
  28. E. Gselmann, Jordan triple mappings on positive definite matrices, Aequationes Math. 89 (2015), 629-639. (pdf)
  29. E. Gselmann, The Lukács-Olkin-Rubin theorem on symmetric cones, submitted.
  30. O. Hatori and L. Molnár, Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in C*-algebras, J. Math. Anal. Appl. 409 (2014), 158-167. (pdf)
  31. O. Hatori and L. Molnár, Generalized isometries of the special unitary group, Arch. Math. 106 (2016), 155-163. (pdf)
  32. O. Hatori and L. Molnár, Spectral conditions for Jordan *-isomorphisms on operator algebras, Studia Math. 236 (2017), 101-126. (pdf)
  33. H. Huang, C.-N. Liu, P. Szokol, M.-C. Tsai and J. Zhang, Trace and determinant preserving maps of matrices, Linear Algebra Appl. 507 (2016), 373-388. (pdf)
  34. Z. Léka, A note on central moments in C*-algebras, J. Math. Inequal. 9 (2015), 165-175. (pdf)
  35. Y. Lim and M. Pálfia, Existence and uniqueness of the L1-Karcher mean, submitted.
  36. L. Molnár, Jordan triple endomorphisms and isometries of unitary groups, Linear Algebra Appl. 439 (2013), 3518-3531. (pdf)
  37. L. Molnár, Bilocal *-automorphisms of B(H), Arch. Math. 102 (2014), 83-89. (pdf)
  38. L. Molnár, A few conditions for a C*-algebra to be commutative, Abstr. Appl. Anal. 2014 (2014), Article ID 705836, 4 pages. (pdf)
  39. L. Molnár, Jordan triple endomorphisms and isometries of spaces of positive definite matrices, Linear Multilinear Algebra 63 (2015), 12-33. (pdf)
  40. L. Molnár, On the nonexistence of order isomorphisms between the sets of all self-adjoint and all positive definite operators, Abstr. Appl. Anal. 2015 (2015), Article ID 705836, 6 pages. (pdf)
  41. L. Molnár, General Mazur-Ulam type theorems and some applications, in Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics, W. Arendt, R. Chill, Y. Tomilov (Eds.), Operator Theory: Advances and Applications, Vol. 250, pp. 311-342, Birkhäuser, 2015. (pdf)
  42. L. Molnár, Two characterizations of unitary-antiunitary similarity transformations of positive definite operators on a finite dimensional Hilbert space, Annales Univ. Sci. Budapest., Sect. Comp. 58 (2015), 83-93. (pdf)
  43. L. Molnár, The logarithmic function and trace zero elements in finite von Neumann factors, Bull. Aust. Math. Soc. 94 (2016), 290-295. (pdf)
  44. L. Molnár, Maps on the positive definite cone of a C*-algebra preserving certain quasi-entropies, J. Math. Anal. Appl. 447 (2017), 206-221. (pdf)
  45. L. Molnár, A characterization of central elements in C*-algebras, Bull. Aust. Math. Soc. 95 (2017), 138-143. (pdf)
  46. L. Molnár, Comment for the "From the Editor-in-Chief" column in LAA, Linear Algebra Appl., to appear. (pdf)
  47. L. Molnár, The arithmetic, geometric and harmonic means in operator algebras and transformations among them, in Recent Methods and Research Advances in Operator Theory, F. Botelho, R. King, T.S.S.R.K. Rao (Eds.), Contemporary Mathematics, Vol. 687, pp. 182-193, American Mathematical Society, 2017. (pdf)
  48. L. Molnár, On the surjectivity of generalized isometries on the positive definite cone of matrices, Mediterr. J. Math. 14:161 (2017). (pdf)
  49. L. Molnár, Algebraic isomorphisms in the descriptions of generalized isometries on spaces of positive definite matrices, submitted. (pdf)
  50. L. Molnár and G. Nagy, Transformations on density operators that leave the Holevo bound invariant, Int. J. Theor. Phys. 53 (2014), 3273-3278. (pdf)
  51. L. Molnár and G. Nagy, Spectral order automorphisms on Hilbert space effects and observables: the 2-dimensional case, Lett. Math. Phys. 106 (2016), 535-544. (pdf)
  52. L. Molnár, G. Nagy and P. Szokol, Maps on density operators preserving quantum f-divergences, Quantum Inf. Process. 12 (2013), 2309-2323. (pdf)
  53. L. Molnár, J. Pitrik and D. Virosztek, Maps on positive definite matrices preserving Bregman and Jensen divergences, Linear Algebra Appl. 495 (2016), 174-189. (pdf)
  54. L. Molnár, P. Šemrl and A.R. Sourour, Bilocal automorphisms, Oper. Matrices 9 (2015), 113-120. (pdf)
  55. L. Molnár and P. Szokol, Transformations on positive definite matrices preserving generalized distance measures, Linear Algebra Appl. 466 (2015), 141-159. (pdf)
  56. L. Molnár and P. Szokol, Transformations preserving norms of means of positive operators and nonnegative functions, Integral Equations Operator Theory 83 (2015), 271-290. (pdf)
  57. L. Molnár and D. Virosztek, On algebraic endomorphisms of the Einstein gyrogroup, J. Math. Phys. 56 (2015), 082302. (pdf)
  58. L. Molnár and D. Virosztek, Continuous Jordan triple endomorphisms of P2, J. Math. Anal. Appl. 438 (2016), 828-839. (pdf)
  59. G. Nagy, Isometries on positive operators of unit norm, Publ. Math. Debrecen 82 (2013), 183-192. (pdf)
  60. G. Nagy, Preserver problems on structures of positive operators, PhD dissertation (2013). (pdf)
  61. G. Nagy, Preservers for the p-norm of linear combinations of positive operators, Abstr. Appl. Anal. 2014 (2014), Article ID 434121, 9 pages. (pdf)
  62. G. Nagy, Isometries of the spaces of self-adjoint traceless operators, Linear Algebra Appl. 484 (2015), 1–12. (pdf)
  63. G. Nagy, Determinant preserving maps: an infinite dimensional version of a theorem of Frobenius, Linear Multilinear Algebra 65 (2017), 351-360. (pdf)
  64. G. Nagy, Isometries of spaces of normalized positive operators under the operator norm, Publ. Math. Debrecen, to appear. (pdf)
  65. M. Pálfia, Operator means of probability measures and generalized Karcher equations, Adv. Math. 289 (2016), 951-1007. (pdf)
  66. M. Pálfia, Löwner's Theorem in several variables, submitted.
  67. P. Szokol, Preserver problems and separation theorems, PhD dissertation (2015). (pdf)
  68. P. Szokol, M.-C. Tsai and J. Zhang, Preserving problems of geodesic-affine maps and related topics on positive definite matrices, Linear Algebra Appl. 483 (2015), 293–308. (pdf)
  69. D. Virosztek, Quantum f-divergence preserving maps on positive semidefinite operators acting on finite dimensional Hilbert spaces, Linear Algebra Appl. 501 (2016), 242-253. (pdf)
  70. D. Virosztek, Quantum entropies, relative entropies, and related preserver problems, PhD dissertation (2016). (pdf)
  71. D. Virosztek, Maps on quantum states preserving Bregman and Jensen divergences, Lett. Math. Phys. 106 (2016)1217-1234. (pdf)
  72. D. Virosztek, Connections between centrality and local monotonicity of certain functions on C*-algebras, J. Math. Anal. Appl. 453 (2017), 221-226. (pdf)
  73. D. Virosztek, A short proof of a duality theorem and another application of an intersection formula on dual cones, submitted.


Reports on the work of the research group (in Hungarian):


  • the time period between July 1, 2012 and June 30, 2013: Word file
  • the time period between July 1, 2013 and June 30, 2014: Word file
  • the time period between July 1, 2014 and June 30, 2015: pdf file
  • the time period between July 1, 2012 and June 30, 2015: pdf file
  • the time period between July 1, 2015 and June 30, 2016: pdf file
  • the time period between July 1, 2012 and June 30, 2017: pdf file


Conferences organized by the research group: