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/Nastava Administrative duties

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

Scientific papers:
  1. Lj. Arambašić, A. Guterman, B. Kuzma, R. Rajić, S. Zhilina, R. Tanaka, Geometric nonlinear classification of Hilbert
    C*-modules based on strong Birkhoff–James orthogonality.     Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 151 (2024). 
  2. Lj. Arambašić, D. Stoeva, Dual frames compensating for erasures - non canonical case, Advances  in Computational Mathematics, Volume 50, article number 9, (2024)
  3. Lj. Arambašić, A. Valent, Strong Birkhoff-James orthogonality of compact operators on Hilbert spaces, accepted in Volume Women in Analysis and PDE, Research Perspectives Ghent Analysis and PDE Center, Birkhäuser, Trends in Mathematics
  4. Lj. Arambašić, D. Stoeva, Constructions of dual frames compensating for erasures with implementations, accepted in Volume Women in Analysis and PDE, Research Perspectives Ghent Analysis and PDE Center, Birkhäuser, Trends in Mathematics
  5. Lj. Arambašić, A. Guterman, B. Kuzma, R. Rajić, S. Zhilina, What does Birkhoff-James orthogonality know about the norm?, Publicationes Mathematicae Debrecen, 102 (1-2), 2023, 197-218.
  6. Lj. Arambašić, A. Valent, On a relation related to strong Birkhoff-James orthogonality, Linear and Multilinear Algebra, 70 (11) (2022), 2088-2096.
  7. 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
  8. 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)
  9. 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.
  10. Lj. Arambašić, I. Gogić, Elementary operators on Hilbert modules over prime C*-algebras, Journal of Mathematical analysis and Applications, 10 pp, 485 (2) (2020)
  11. Lj. Arambašić, R. Rajić, Another characterization of orthogonality in Hilbert C*-modules, Mathematical Inequalities and Applications, 22(4) (2019), 1421-1426.
  12. Lj. Arambašić, R. Rajić, Roberts orthogonality for 2x2 complex matrices, Acta Mathematica Hungarica 157 (2019) (1),  220-228.
  13. Lj. Arambašić, On approximately dual frames for Hilbert C*-modules, Filomat 33:12 (2019), 3869-3875.
  14. Lj. Arambašić, D. Bakić, Full spark frames and totally positive matrices, Linear and Multilinear Algebra, 67 (8) (2019), 1685-1700.
  15. Lj. Arambašić, R. Rajić, On Birkhoff-James and Roberts orthogonality, Special Matrices 6 (2018) , 229-236
  16. Lj. Arambašić, T. Berić, R. Rajić, Roberts orthogonality and Davis-Wielandt shell, Linear algebra and its Applications, 539 (2018), 1-13.
  17. Lj. Arambašić, D. Bakić, Dual frames compansating for erasures, Glasnik Matematički, 52 (2017)(1), 131-146.
  18. Lj. Arambašić, D. Bakić, Frames and outer frames for Hilbert C*-modules, Linear and multilinear algebra 65 (2017) (2), 381-431., arXiv:1507.04101v1
  19. 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.
  20. Lj. Arambašić, R. Rajić, Operators preserving the strong Birkhoff-James orthogonality on B(H), Linear Algebra and its Applications, 471 (2015), 394--404.
  21. Lj. Arambašić, R. Rajić, On three concepts of orthogonality in Hilbert C*-modules, Linear and Multilinear Algebra 63 (2015), no. 7, 1485-1500.
  22. 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.
  23. 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.
  24. Lj. Arambašić, R. Rajić, The Birkhoff--James orthogonality in Hilbert C*-modules, Linear Algebra and its Applications 437 (2012)  7; 1913-1929.
  25. 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.
  26. Lj. Arambašić, D. Bakić, R. Rajić, Finite-dimensional Hilbert C*-modules, Banach Journal of Mathematical Analysis, 4 (2010), no. 2, 147-157.
  27. Lj. Arambašić, D. Bakić, R. Rajić, Dimension functions, scaling sequences, and wavelet sets, Studia Math. 198 (2010), 1-32.
  28. 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,
  29. Lj. Arambašić, R. Rajić, Ostrowski’ s inequality in pre-Hilbert C*-modules, Mathematical Inequalities and Applications 12 (2009), 1; 217-226.
  30. Lj. Arambašić, Another characterization of Hilbert C*-modules over compact operators, Journal of Mathematical Analysis and Applications 344 (2008), 2; 735-740.
  31. Lj. Arambašić, R. Rajić, On the C*-valued triangle equality and inequality in Hilbert C*-modules, Acta Mathematica Hungarica 119 (2008), 4; 373-380.
  32. Lj. Arambašić, D. Bakić, R. Rajić, Dimension functions of orthonormal wavelets, Journal of Fourier Analysis and Applications 13 (2007), 3; 331-356.
  33. Lj. Arambašić, On frames for countably generated Hilbert C*-modules, Proceedings of the American Mathematical Society 135 (2007), 2; 469-478.
  34. Lj. Arambašić, R. Rajić, On some norm equalities in pre-Hilbert C*-module, Linear Algebra and its Applications 414 (2006), 1; 19-28.
  35. Lj. Arambašić, Frames of submodules for countably generated Hilbert K(H)-modules, Glasnik Matematički 41 (2006), 2; 317-328.
  36. Lj. Arambašić, Irreducible representations of Hilbert C*-modules, Mathematical Proceedings of the Royal Irish Academy 105A (2005), 2; 11-24.
Book chapter:
  • Lj. Arambašić, A. Guterman, B. Kuzma, S. Zhilina: Birkhoff-James orthogonality: characterizations, preservers, and orthogonality graph, a chapter in Operator and norm inequalities and related topics, 1st ed. 2022, Springer, Trends in Mathematics, 255-302.
Professional papers (In Croatian)
  1. Lj. Arambašić, K. Dujlović, M. Pleša, Z. Posavec, Učenje istraživanjem i pričanjem priče, Poučak, 2024.
  2. Lj. Arambašić, L. Crnobrnja, Determinante (Determinants), Poučak: časopis za metodiku i nastavu matematike,  22 (87) (2021), 36-50. 
  3. Lj. Arambašić, Hamilton-Cayleyjev teorem za matrice reda 2 (The Hamilton-Cayley theorem for matrices of order 2), Poučak 20 (80) (2019) 34-40.
  4. 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. 
  5. Lj. Arambašić, M. Kolarek, Napeti bazni okviri (Tight frames), Poučak 20 (77) (2019) 29-38.
  6. Lj. Arambašić, R. Rajić, Dva zadatka o najkraćem putu (Two tasks on the shorthest path), Poučak 19 (75) (2018) 4-8.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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/conferences:
Conference organization:
Membership in editorial boards:
 Reviewing for Mathematical Reviews, ZbMATH and many scientific journals.