Ljiljana Arambašić
Professor
University of Zagreb
Faculty of Science
Department of Mathematics
Bijenička cesta 30, 10000  Zagreb, Croatia
phone: ++ 385 1 46 05 893
email: arambas_at_math.hr
office: A314
Ljiljana

Home Research Teaching (in Croatian) Administrative duties


Zagreb Workshop on Operator Theory 2020 June 29-30 (online)


My research interests include  C*-algebras, Hilbert C*-modules, frames in Hilbert spaces and Hilbert C*-modules,  various types of orthogonality, orthogonality preservers....

Book chapter:
  • Lj. Arambašić, A. Guterman, B. Kuzma, S. Zhilina: Birkhoff-James orthogonality: characterizations, preservers, and orthogonality graph, preprint
Scientific papers:
  1. Lj. Arambašić, A. Guterman, B. Kuzma, R. Rajić, S. Zhilina, What does Birkhoff-James orthogonality know about the norm?, preprint
  2. Lj. Arambašić, D. Stoeva, Dual frames compensating for erasures - non canonical case, preprint
  3. Lj. Arambašić, A. Guterman, B. Kuzma, R. Rajić, S. Zhilina, Operators preserving mutual strong Birkhoff-James orthogonality on B(H), Linear Algebra and its Applications, 624 (2021), 27-43
  4. Lj. Arambašić, A. Guterman, B. Kuzma, R. Rajić, S. Zhilina, Symmetrized Birkhoff-James orthogonality in arbitrary normed spaces, Journal of Mathematical Analysis and Applications, 16 pp,  502 (1), (2021)
  5. Lj. Arambašić, A. Valent, On a relation related to strong Birkhoff-James orthogonality, accepted for publication in  Linear and Multilinear Algebra
  6. Lj. Arambašić, A. Guterman, B. Kuzma, R. Rajić, S. Zhilina, Orthograph related to mutual strong Birkhoff-James orthogonality in C*-algebras, Banach Journal of Mathematical Analysis, 14 (4) (2020), 1751-1772.
  7. Lj. Arambašić, I. Gogić, Elementary operators on Hilbert modules over prime C*-algebras, Journal of Mathematical analysis and Applications, 10 pp, 485 (2) (2020)
  8. Lj. Arambašić, R. Rajić, Another characterization of orthogonality in Hilbert C*-modules, Mathematical Inequalitis and Applications, 22(4) (2019), 1421-1426.
  9. Lj. Arambašić, R. Rajić, Roberts orthogonality for 2x2 complex matrices, Acta Mathematica Hungarica 157 (2019) (1),  220-228.
  10. Lj. Arambašić, On approximately dual frames for Hilbert C*-modules, Filomat 33:12 (2019), 3869-3875.
  11. Lj. Arambašić, D. Bakić, Full spark frames and totally positive matrices, Linear and Multilinear Algebra, 67 (8) (2019), 1685-1700.
  12. Lj. Arambašić, R. Rajić, On Birkhoff-James and Roberts orthogonality, Special Matrices 6 (2018) , 229-236
  13. Lj. Arambašić, T. Berić, R. Rajić, Roberts orthogonality and Davis-Wielandt shell, Linear algebra and its Applications, 539 (2018), 1-13.
  14. Lj. Arambašić, D. Bakić, Dual frames compansating for erasures, Glasnik Matematički, 52 (2017)(1), 131-146.
  15. Lj. Arambašić, D. Bakić, Frames and outer frames for Hilbert C*-modulesLinear and multilinear algebra 65 (2017) (2), 381-431., arXiv:1507.04101v1
  16. Lj. Arambašić, R. Rajić, On symmetry of the (strong) Birkhoff--James orthogonality in Hilbert C*-modules, Annals of Functional Analysis 7 (2016), no. 1., 17--23.
  17. Lj. Arambašić, R. Rajić, Operators preserving the strong Birkhoff-James orthogonality on B(H), Linear Algebra and its Applications, 471 (2015), 394--404.
  18. Lj. Arambašić, R. Rajić, On three concepts of orthogonality in Hilbert C*-modules, Linear and Multilinear Algebra 63 (2015), no. 7, 1485-1500.
  19. Lj. Arambašić, R. Rajić, Operator version of the best approximation problem in Hilbert C*-modules, Journal of Mathematical Analysis and Applications, 413 (2014), 1; 311-320.
  20. Lj. Arambašić, R. Rajić, A strong version of the Birkhoff--James orthogonality in Hilbert C*-modules, Annals of Functional Analysis 5 (2014),  no. 1, 109-120.
  21. Lj. Arambašić, R. Rajić, The Birkhoff--James orthogonality in Hilbert C*-modules, Linear Algebra and its Applications 437 (2012)  7; 1913-1929.
  22. Lj. Arambašić, D. Bakić, M.S. Moslehian, A treatment of the Cauchy-Schwarz inequality in C*-modules, Journal of Mathematical Analysis and Applications 381 (2011) 2; 546-556.
  23. Lj. Arambašić, D. Bakić, R. Rajić, Finite-dimensional Hilbert C*-modules, Banach Journal of Mathematical Analysis, 4 (2010), no. 2, 147-157.
  24. Lj. Arambašić, D. Bakić, R. Rajić, Dimension functions, scaling sequences, and wavelet sets, Studia Math. 198 (2010), 1-32.
  25. Lj. Arambašić, D. Bakić, M.S. Moslehian, A characterization of Hilbert C*-modules over finite dimensional C*-algebras, Operators and Matrices 3 (2009), 2; 235-240,
  26. Lj. Arambašić, R. Rajić, Ostrowski’ s inequality in pre-Hilbert C*-modules, Mathematical Inequalities and Applications 12 (2009), 1; 217-226.
  27. Lj. Arambašić, Another characterization of Hilbert C*-modules over compact operators, Journal of Mathematical Analysis and Applications 344 (2008), 2; 735-740.
  28. Lj. Arambašić, R. Rajić, On the C*-valued triangle equality and inequality in Hilbert C*-modules, Acta Mathematica Hungarica 119 (2008), 4; 373-380.
  29. Lj. Arambašić, D. Bakić, R. Rajić, Dimension functions of orthonormal wavelets, Journal of Fourier Analysis and Applications 13 (2007), 3; 331-356.
  30. Lj. Arambašić, On frames for countably generated Hilbert C*-modules, Proceedings of the American Mathematical Society 135 (2007), 2; 469-478.
  31. Lj. Arambašić, R. Rajić, On some norm equalities in pre-Hilbert C*-module, Linear Algebra and its Applications 414 (2006), 1; 19-28.
  32. Lj. Arambašić, Frames of submodules for countably generated Hilbert K(H)-modules, Glasnik Matematički 41 (2006), 2; 317-328.
  33. Lj. Arambašić, Irreducible representations of Hilbert C*-modules, Mathematical Proceedings of the Royal Irish Academy 105A (2005), 2; 11-24.
Professional papers (In Croatian)
  1. Lj. Arambašić, L. Crnobrnja, Determinante (Determinants), Poučak: časopis za metodiku i nastavu matematike,  22 (87) (2021), 36-50. 
  2. Lj. Arambašić, Hamilton-Cayleyjev teorem za matrice reda 2 (The Hamilton-Cayley theorem for matrices of order 2), Poučak 20 (80) (2019) 34-40.
  3. Lj. Arambašić, M. Horvat, Malo kompleksne analize i osnovni teorem algebre (Some complex analysis and the fundamental theorem of algebra), Acta mathematica Spalatensia. Series didactica, Vol. 2 (2019) 57-66. 
  4. Lj. Arambašić, M. Kolarek, Napeti bazni okviri (Tight frames), Poučak 20 (77) (2019) 29-38.
  5. Lj. Arambašić, R. Rajić, Dva zadatka o najkraćem putu (Two tasks on the shorthest path), Poučak 19 (75) (2018) 4-8.
  6. Lj. Arambašić, M. Matika, A. Valent, Neke generalizacije Rolleovog teorema i Lagrangeovog teorema srednje vrijednosti (Some generalizations of Rolle's theorem and Lagrange's mean value theorem), Poučak: časopis za metodiku i nastavu matematike,  16 (61) (2015), 14-21.
  7. Lj. Arambašić, R. Rajić, Duljina puta od n segmenata (The length of a path consisting of n line segments), Poučak: časopis za metodiku i nastavu matematike 14 (56) (2013), 34-39.
  8. Lj. Arambašić, A. Valent, Neke primjene Rolleovog. .-teorema i Lagrangeovog teorema srednje vrijednosti (Some applications of Rolle's theorem and Lagrange's mean value theorem), Poučak: časopis za metodiku i nastavu matematike, 14 (55) (2013), 47-56.
  9. Lj. Arambašić, A. Kralj, Razni dokazi Cauchy-Schwarz-Bunjakovskijeve nejednakosti (Various proofs of Cauchy-Schwarz-Bunjakovski inequality), Poučak: časopis za metodiku i nastavu matematike,  51 (2012), 32-38.
  10. Lj. Arambašić, I. Zavišić, p-norme na R^2, kružnice S_p i brojevi \pi_p (p-norms on R^2, S_p circles and \pi_p numbers),  Osječki matematički list, 10, (2010) 131-138.
  11. Lj. Arambašić, V. Seuček, O neprekidnim funkcijama (On continuous functions), Poučak: časopis za metodiku i nastavu matematike, 41, (2010) 50-60. 
Projects/grants:
  • Frames, reconstruction, and applications, Austria-Croatia bilateral project (principal investigator with Diana Stoeva, 2020-2022)
  • Parseval frames for Hilbert spaces and Hilbert C*-modules by University of Zagreb (2018)
  • Operators on C*-algebra and Hilbert modules, by Croatian Science Foundation (investigator, 2017-2021)
  • Frames for Hilbert spaces and Hilbert C*-modules by University of Zagreb (2017)
  • Frames for Hilbert C*-modules by University of Zagreb (2016)
  • Hilbert C*-modules by University of Zagreb (2015)
  • Students' understanding of graphs in mathematics and physics  by University of Zagreb (2014)
  • C*-algebras and Hilbert C*-modules by University of Zagreb (2014)
  • Orthonormal wavelets and generalized multiresolution analyses by Ministry of Science, Education and Sports of the Republic of Croatia (investigator, 2007-2014, principal investigator Damir Bakić) 
  • Hilbert modules and operator spaces by Ministry of Science, Education and Sports of the Republic of Croatia (investigator, 2002-2006, principal investigator Boris Guljaš)
  • Applications of approximations in geometrical topology by Ministry of Science, Education and Sports of the Republic of Croatia (investigator, 2000-2002, principal investigator Zvonko Čerin)
Talks:
Conference organization:
Membership in editorial boards:
Reviewing for:
  • Mathematical Reviews
  • ZbMATH
  • many scientific journals