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

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

List of publications:
  1. Full spark frames and totally positive matrices (with D. Bakić), preprint
  2. Roberts orthogonality and Davis-Wielandt shell (with T. Berić and R. Rajić), Linear algebra and its Applications, 539 (2018), 1-13.
  3. Dual frames compansating for erasures (with D. Bakić), Glasnik Matematički, 52 (2017)(1), 131-146.
  4. Frames and outer frames for Hilbert C*-modules (with D. Bakić)Linear and multilinear algebra 65 (2017) (2), 381-431., arXiv:1507.04101v1
  5. On symmetry of the (strong) Birkhoff--James orthogonality in Hilbert C*-modules (with R. Rajić), Annals of Functional Analysis 7 (2016), no. 1., 17--23.
  6. Operators preserving the strong Birkhoff-James orthogonality on B(H) (with R. Rajić), Linear Algebra Appl. 471 (2015), 394--404.
  7. On three concepts of orthogonality in Hilbert C*-modules (with R. Rajić), Linear and Multilinear Algebra 63 (2015), no. 7, 1485-1500.
  8. Operator version of the best approximation problem in Hilbert C*-modules (with R. Rajić), Journal of Mathematical Analysis and Applications, 413 (2014), 1; 311-320.
  9. A strong version of the BirkhoAff--James orthogonality in Hilbert C*-modules (with R. Rajić), Annals of Functional Analysis 5 (2014),  no. 1, 109-120.
  10. The Birkhoff--James orthogonality in Hilbert C*-modules (with R. Rajić), Linear Algebra and its Applications 437 (2012)  7; 1913-1929.
  11. A treatment of the Cauchy-Schwarz inequality in C*-modules (with D. Bakić and  M. S. Moslehian), Journal of Mathematical Analysis and Applications 381 (2011) 2; 546-556.
  12. Finite-dimensional Hilbert C*-modules (with D. Bakić and R. Rajić), Banach Journal of Mathematical Analysis, 4 (2010), no. 2, 147-157.
  13. Dimension functions, scaling sequences, and wavelet sets (with D. Bakić and R. Rajić), Studia Math. 198 (2010), 1-32.
  14. A characterization of Hilbert C*-modules over finite dimensional C*-algebras (with D. Bakić and  M. S. Moslehian), Operators and Matrices 3 (2009), 2; 235-240,
  15. Ostrowski’ s inequality in pre-Hilbert C*-modules (with R. Rajić), Mathematical Inequalities and Applications 12 (2009), 1; 217-226.
  16. Another characterization of Hilbert C*-modules over compact operators, Journal of Mathematical Analysis and Applications 344 (2008), 2; 735-740.
  17. On the C*-valued triangle equality and inequality in Hilbert C*-modules (with R. Rajić), Acta Mathematica Hungarica 119 (2008), 4; 373-380.
  18. Dimension functions of orthonormal wavelets (with D. Bakić and R. Rajić), Journal of Fourier Analysis and Applications 13 (2007), 3; 331-356.
  19. On frames for countably generated Hilbert C*-modules, Proceedings of the American Mathematical Society 135 (2007), 2; 469-478.
  20. On some norm equalities in pre-Hilbert C*-module (with R. Rajić), Linear Algebra and its Applications 414 (2006), 1; 19-28.
  21. Frames of submodules for countably generated Hilbert K(H)-modules, Glasnik Matematički 41 (2006), 2; 317-328.
  22. 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: