Ljiljana Arambašić
Professor

Department of Mathematics
Bijenička cesta 30
10000  Zagreb, Croatia

phone: ++ 385 1 46 05 893
email: arambas_at_math.hr
office: A314

ljiljana2

Home Research Teaching (in Croatian)


My research interests include
 C*-algebras, Hilbert C*-modules, frames in Hilbert spaces and Hilbert C*-modules, orthonormal wavelets,...

List of publications:
  1. Lj. Arambašić, R. Rajić, Roberts orthogonality for 2x2 complex matrices, accepted for publication in Acta Mathematica Hungarica
  2. Lj. Arambašić, On approximately dual frames for Hilbert C*-modules, accepted for publication in Filomat
  3. Lj. Arambašić, D. Bakić, Full spark frames and totally positive matrices, accepted for publication in Linear and Multilinear Algebra
  4. Lj. Arambašić, R. Rajić, On Birkhoff-James and Roberts orthogonality, Special Matrices 6 (2018) , 229-236
  5. Lj. Arambašić, T. Berić, R. Rajić, Roberts orthogonality and Davis-Wielandt shell, Linear algebra and its Applications, 539 (2018), 1-13.
  6. Lj. Arambašić, D. Bakić, Dual frames compansating for erasures, Glasnik Matematički, 52 (2017)(1), 131-146.
  7. Lj. Arambašić, D. Bakić, Frames and outer frames for Hilbert C*-modulesLinear and multilinear algebra 65 (2017) (2), 381-431., arXiv:1507.04101v1
  8. 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.
  9. Lj. Arambašić, R. Rajić, Operators preserving the strong Birkhoff-James orthogonality on B(H), Linear Algebra and its Applications, 471 (2015), 394--404.
  10. Lj. Arambašić, R. Rajić, On three concepts of orthogonality in Hilbert C*-modules, Linear and Multilinear Algebra 63 (2015), no. 7, 1485-1500.
  11. 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.
  12. Lj. Arambašić, R. Rajić, A strong version of the BirkhoAff--James orthogonality in Hilbert C*-modules, Annals of Functional Analysis 5 (2014),  no. 1, 109-120.
  13. Lj. Arambašić, R. Rajić, The Birkhoff--James orthogonality in Hilbert C*-modules, Linear Algebra and its Applications 437 (2012)  7; 1913-1929.
  14. 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.
  15. Lj. Arambašić, D. Bakić, R. Rajić, Finite-dimensional Hilbert C*-modules, Banach Journal of Mathematical Analysis, 4 (2010), no. 2, 147-157.
  16. Lj. Arambašić, D. Bakić, R. Rajić, Dimension functions, scaling sequences, and wavelet sets, Studia Math. 198 (2010), 1-32.
  17. 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,
  18. Lj. Arambašić, R. Rajić, Ostrowski’ s inequality in pre-Hilbert C*-modules, Mathematical Inequalities and Applications 12 (2009), 1; 217-226.
  19. Lj. Arambašić, Another characterization of Hilbert C*-modules over compact operators, Journal of Mathematical Analysis and Applications 344 (2008), 2; 735-740.
  20. Lj. Arambašić, R. Rajić, On the C*-valued triangle equality and inequality in Hilbert C*-modules, Acta Mathematica Hungarica 119 (2008), 4; 373-380.
  21. Lj. Arambašić, D. Bakić, R. Rajić, Dimension functions of orthonormal wavelets, Journal of Fourier Analysis and Applications 13 (2007), 3; 331-356.
  22. Lj. Arambašić, On frames for countably generated Hilbert C*-modules, Proceedings of the American Mathematical Society 135 (2007), 2; 469-478.
  23. Lj. Arambašić, R. Rajić, On some norm equalities in pre-Hilbert C*-module, Linear Algebra and its Applications 414 (2006), 1; 19-28.
  24. Lj. Arambašić, Frames of submodules for countably generated Hilbert K(H)-modules, Glasnik Matematički 41 (2006), 2; 317-328.
  25. Lj. Arambašić, Irreducible representations of Hilbert C*-modules, Mathematical Proceedings of the Royal Irish Academy 105A (2005), 2; 11-24.
Projects:
  • Operators on C*-algebra and Hilbert modules, by Croatian Science Foundation (investigator, 2017-, principal investigator Damir Bakić)
  • Frames for Hilbert spaces and Hilbert C*-modules by University of Zagreb, (principal investigator, 2017)
  • Frames for Hilbert C*-modules by University of Zagreb, (principal investigator, 2016)
  • Hilbert C*-modules by University of Zagreb, (investigator, 2015, principal investigator Damir Bakić )
  • Students' understanding of graphs in mathematics and physics  by University of Zagreb (investigator, 2014, principal investigator Maja Planinić)
  • C*-algebras and Hilbert C*-modules by University of Zagreb (investigator, 2014, principal investigator Dijana Ilišević)
  • 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)
Conferences: