Ilja Gogić

Curriculum Vitae

English (PDF) / Hrvatski (PDF)

Education

• Ph.D. in Mathematics: June 2, 2010, Department of Mathematics, University of Zagreb
  Dissertation title: Completely bounded maps and subhomogeneous C*-algebras (in Croatian)
  Advisor: Prof. Bojan Magajna (co-advisor: Prof. Damir Bakić)
• B.Sc. in Mathematics: January 12, 2005, Department of Mathematics, University of Zagreb
  Diploma Thesis: K-Theory for C*-algebras (in Croatian)
  Advisor: Prof. Hrvoje Kraljević

Fields of Interest

• Operator algebras
  • General theory of C*-algebras and von Neumann algebras
  • Automorphisms, derivations, local multipliers, and elementary operators on C*-algebras
  • The Dixmier property and weak centrality for C*-algebras
• Noncommutative and nonassociative algebras
  • Characterizations of Jordan homomorphisms through preserving properties
  • Multiplicative maps on nonassociative algebras and automatic additivity
  • Algebraic variations of problems in operator algebras

Research Papers and Preprints full list

Preprints

• The structure of k-potents and mixed Jordan-power preservers on matrix algebras (with M. Tomašević), [arXiv: 2512.13085]
• Continuous spectrum-shrinking maps and applications to preserver problems (with A. Chirvasitu and M. Tomašević), [arXiv: 2501.06840]

Research Papers

• Continuous spectrum-shrinking maps between finite-dimensional algebras (with M. Tomašević), to appear in J. Algebra Appl., [DOI: 10.1142/S0219498826502981]
• Classification of Jordan multiplicative maps on matrix algebras (with M. Tomašević), Aequat. Math., 99 (2025), 2339–2355, [DOI: 10.1007/s00010-025-01208-y]
• Multiplicative and Jordan multiplicative maps on structural matrix algebras (with M. Tomašević), Linear Multilinear Algebra, 73 (2025), 4131-4148, [DOI: 10.1080/03081087.2025.2590557]
• A variant of Šemrl's preserver theorem for singular matrices (with A. Chirvasitu and M. Tomašević), Linear Algebra Appl., 724 (2025), 298-319, [DOI: 10.1016/j.laa.2025.06.021]
• An extension of Petek-Šemrl preserver theorems for Jordan embeddings of structural matrix algebras (with M. Tomašević), J. Math. Anal. Appl., 549 (2025), 129497, [DOI: 10.1016/j.jmaa.2025.129497]
• Jordan embeddings and linear rank preservers of structural matrix algebras (with M. Tomašević), Linear Algebra Appl., 707 (2025), 1-48, [DOI: 10.1016/j.laa.2024.11.013]
• Characterizing Jordan embeddings between block upper-triangular subalgebras via preserving properties (with T. Petek and M. Tomašević), Linear Algebra Appl., 704 (2025), 192-217, [DOI: 10.1016/j.laa.2024.10.005]
• Local variants of the Dixmier property and weak centrality for C*-algebras (with R. J. Archbold and L. Robert), Int. Math. Res. Not. IMRN, 2 (2023), 1483–1513, [DOI: 10.1093/imrn/rnab275]
• The centre-quotient property and weak centrality for C*-algebras (with R. J. Archbold), Int. Math. Res. Not. IMRN, 2 (2022), 1173–1216, [DOI: 10.1093/imrn/rnaa133]
• The cb-norm approximation of generalized skew derivations by elementary operators, Linear Multilinear Algebra, 69 (2021), 1543-1556, [DOI: 10.1080/03081087.2019.1632784]
• On the ideal structure of the tensor product of nearly simple algebras, Comm. Algebra, 48 (2020), 2248-2257, [DOI: 10.1080/00927872.2019.1710842]
• Elementary operators on Hilbert modules over prime C*-algebras (with Lj. Arambašić), J. Math. Anal. Appl., 485 (2020), 123861, [DOI: 10.1016/j.jmaa.2020.123861]
• Centrally stable algebras (with M. Brešar), J. Algebra, 537 (2019), 79-97, [DOI: 10.1016/j.jalgebra.2019.06.041]
• The closure of two-sided multiplications on C*-algebras and phantom line bundles (with R. M. Timoney), Int. Math. Res. Not. IMRN, 2 (2018), 607-640, [DOI: 10.1093/imrn/rnw248]
• On unital C(X)-algebras and C(X)-valued conditional expectations of finite index (with E. Blanchard), Linear Multilinear Algebra, 64 (2016), 2406-2418, [DOI: 10.1080/03081087.2016.1158231]
• Generalized skew derivations implemented by elementary operators (with D. Eremita and D. Ilišević), Algebr. Represent. Theory, 17 (2014), 983-996, [DOI: 10.1007/s10468-013-9429-8]
• The local multiplier algebra of a C*-algebra with finite dimensional irreducible representations, J. Math. Anal. Appl., 408 (2013), 789-794, [DOI: 10.1016/j.jmaa.2013.06.036]
• Derivations of subhomogeneous C*-algebras are implemented by local multipliers, Proc. Amer. Math. Soc., 141 (2013), 3925-3928, [DOI: 10.1090/S0002-9939-2013-11762-4]
• On derivations and elementary operators on C*-algebras, Proc. Edinb. Math. Soc., 56 (2013), 515-534, [DOI: 10.1017/S0013091512000302]
• Topologically finitely generated Hilbert C(X)-modules, J. Math. Anal. Appl., 395 (2012), 559-568, [DOI: 10.1016/j.jmaa.2012.05.050]
• Elementary operators and subhomogeneous C*-algebras II, Banach J. Math. Anal., 5 (2011), 181-192, [DOI: 10.15352/bjma/1313362989]
• Elementary operators and subhomogeneous C*-algebras, Proc. Edinb. Math. Soc., 54 (2011), 99-111, [DOI: 10.1017/S0013091509001114]
• Derivations which are inner as completely bounded maps, Oper. Matrices, 4 (2010), 193-211, [DOI: 10.7153/oam-04-09]

Talks

Conference and Workshop Talks

• The Dixmier property and weak centrality for C*-algebras, 8th Croatian Mathematical Congress. Osijek, Croatia — July 2–5, 2024.
• Applications of algebraic topology to operator algebras: Homogeneous C*-algebras, XXII Geometrical Seminar. Vrnjačka Banja, Serbia — May 26–31, 2024.
• Applications of algebraic topology to operator algebras: Homogeneous C*-algebras, Kick-off meeting of CA21109 COST Action CaLISTA. Bologna, Italy — June 5–9, 2023.
• On noncommutative branched coverings, XXI Geometrical Seminar. Belgrade, Serbia — June 26–July 2, 2022.
• Elementary operators on C*-algebras and Hilbert C*-modules, The 49th Canadian Operator Symposium. University of Guelph — May 31–June 4, 2021 (online).
• On automorphisms, derivations and elementary operators of C*-algebras, Great Plains Operator Theory Symposium 2021. Washington University in St. Louis — May 10–14, 2021 (online).
• Elementary operators on Hilbert C*-modules, International Workshop Hilbert C*-Modules Online Weekend. December 5–6, 2020 (online).
• Centrally stable algebras, 2nd Zagreb Workshop on Operator Theory. University of Zagreb — June 29–30, 2020 (online).
• The centre-quotient property and weak centrality for C*-algebras, The 48th Canadian Operator Symposium. The Fields Institute — May 25–29, 2020 (online).
• The cb-norm approximation of derivations and automorphisms by elementary operators, IWOTA 2019. Lisbon, Portugal — July 22–26, 2019.
• The cb-norm approximations by two-sided multiplications and elementary operators, Analysis, Geometry and Algebra. Trinity College Dublin — May 8–10, 2019.
• The cb-norm approximation of generalized skew derivations by elementary operators, Workshop: Operator days. Zagreb, Croatia — January 31–February 1, 2019.
• On unital C(X)-algebras and C(X)-valued conditional expectations of finite index, The ninth Symposium "Mathematics and Applications" 2018. Belgrade, Serbia — November 30–December 1, 2018.
• Fiberwise two-sided multiplications on homogeneous C*-algebras, 27th International Conference in Operator Theory. Timișoara, Romania — July 2–6, 2018.
• Fiberwise two-sided multiplications on homogeneous C*-algebras, XX Geometrical Seminar. Vrnjačka Banja, Serbia — May 20–23, 2018.
• Two-sided multiplications and phantom line bundles, 19th Geometrical Seminar. Zlatibor, Serbia — August 28–September 4, 2016.
• When are the lengths of elementary operators uniformly bounded?, IWOTA 2015. Tbilisi, Georgia — July 6–10, 2015.
• When are the two-sided multiplication maps norm-closed?, 43rd Canadian Operator Symposium on Operator Theory and Operator Algebras. University of Waterloo — June 15–19, 2015.
• CB-norm approximation of derivations by elementary operators, Great Plains Operator Theory Symposium 2015. Purdue University — May 26–30, 2015.
• On derivations and elementary operators on C*-algebras, Infinite Dimensional Function Theory: Present Progress and Future Problems. University College Dublin — January 8–9, 2015.
• C(X)-algebras as noncommutative branched covering, Masterclass on Classification, STructure, Amenability and Regularity. University of Glasgow — August 25–29, 2014.
• Topologically finitely generated Hilbert C(X)-modules, Days of Analysis in Novi Sad. University of Novi Sad — July 3–7, 2014.
• C(X)-algebras as noncommutative branched covering, Zagreb Workshop on Operator Theory. University of Zagreb — July 3–4, 2014.
• Derivations and local multipliers of C*-algebras, Great Plains Operator Theory Symposium 2014. Kansas State University — May 27–31, 2014.
• Finitely C(X)-generated continuous C(X)-algebras, Young Functional Analysts' Meeting 2014. University of Debrecen — April 11–13, 2014.
• The local multiplier algebra of a C*-algebra with finite dimensional irreducible representations, Banach Algebras and Applications. University of Gothenburg — July 29–August 4, 2013.
• On Automorphisms, Derivations and Elementary Operators, The 4th Novi Sad Algebraic Conference & Semigroups and Applications 2013. University of Novi Sad — June 5–9, 2013.
• Topologically finitely generated Hilbert C(X)-modules, 24th International Conference on Operator Theory. The West University of Timișoara — July 2–7, 2012.
• Elementary operators and subhomogeneous C*-algebras, Banach Algebras 2011. University of Waterloo — August 3–10, 2011.
• Finitely centrally generated C*-algebras, Applied Linear Algebra. University of Novi Sad — May 24–28, 2010.
• Derivations, completely bounded maps and the ideal structure of C*-algebras, Operators, Spaces, Algebras, Modules. University of Zagreb — March 1–4, 2010.

Seminar and Colloquium Talks

• The Dixmier property and weak centrality for C*-algebras, Algebra and Functional Analysis Seminar. University of Ljubljana — January 8, 2026.
• Spectrum-shrinking maps and nonlinear preservers on matrix domains, European Non-Associative Algebra Seminar. October 13, 2025 (online).
• Derivations on C*-Algebras: A Revisit, Logic, Categories, and Applications Seminar. University of Bologna — June 13, 2025.
• Centrally stable algebras, Mathematical Colloquium. Mathematical Institute of SASA, Belgrade — June 20, 2019.
• Local multipliers and elementary operators of C*-algebras, Operator Theory Seminar. University of Belgrade — June 20, 2019.
• Finitely C(X)-generated continuous C(X)-algebras, Seminar on Geometry, Education and Visualization with Applications. Mathematical Institute of SASA, Belgrade — November 29, 2018.
• The cb-norm approximation of generalized skew derivations by elementary operators, Operator Theory Seminar. University of Belgrade — November 29, 2018.
• Fiberwise two-sided multiplications and the second Čech cohomology, Combinatorics, Geometry, Topology and Algebra Seminar. University of Belgrade — November 27, 2018.
• The cb-norm approximation of generalized skew derivations by elementary operators, Functional Analysis and Algebra Seminar. University of Ljubljana — November 22, 2018.
• When are the lengths of elementary operators uniformly bounded?, Analysis Seminar. Trinity College Dublin — February 9, 2016.
• Uniform approximation by two-sided multiplication maps, Analysis Seminar. Trinity College Dublin — October 27, 2015.
• Uniform approximation by two-sided multiplication maps on C*-algebras M_n(C(X)), Combinatorics, Geometry, Topology and Algebra Seminar. University of Belgrade — June 26, 2015.
• CB-norm approximation of derivations by elementary operators, Analysis Seminar. University of Glasgow — March 3, 2015.
• Noncommutative branched coverings, Analysis Seminar. Trinity College Dublin — January 27, 2015.
• Derivations, elementary operators and local multipliers of C*-algebras, Functional Analysis and Algebra Seminar. University of Ljubljana — February 27, 2014.
• Elementary operators on homogeneous C*-algebras, Combinatorics, Geometry, Topology and Algebra Seminar. University of Belgrade — February 25, 2014.
• C(X)-valued conditional expectations of finite index, Seminar for Analysis and Foundations of Mathematics. University of Novi Sad — December 9, 2013.
• Homogeneous C*-algebras, Combinatorics, Geometry, Topology and Algebra Seminar. University of Belgrade — December 3, 2013.
• Topological and C*-algebraic K-theory, Seminar for Analysis and Foundations of Mathematics. University of Novi Sad — December 2, 2013.
• C*-algebras as noncommutative topology, Seminar for Analysis and Foundations of Mathematics. University of Novi Sad — November 25, 2013.
• Apllications of fibre bundles to C*-algebras, Seminar on Geometry, Education and Visualization with Applications. Mathematical Institute of SASA, Belgrade — November 21, 2013.
• Noncommutative branched coverings, Mathematical Colloquium. Mathematical Institute of SASA, Belgrade — November 8, 2013.
• Derivations of C*-algebras and local multipliers, Mathematical Colloquium of Osijek Mathematical Society. University of Osijek — April 11, 2013.
• Derivations of C*-algebras and local multipliers, Scientific Colloquium of Croatian Mathematical Society. University of Zagreb — January 30, 2013.
• Derivations implemented by local multipliers, Seminar for Analysis and Foundations of Mathematics. University of Novi Sad — October 29, 2012.
• On derivations and elementary operators on C*-algebras, Analysis Seminar, University of Aberdeen — November 4, 2011.
• Topologically finitely generated Hilbert C(X)-modules, Analysis Seminar. Trinity College Dublin — November 1, 2011.
• Elementary operators and subhomogeneous C*-algebras, Functional Analysis and Algebra Seminar. University of Ljubljana — April 16, 2010.

Teaching (in Croatian)

Fakultativni kolegij

Studentska natjecanja iz matematike

• Oktonioni i Hurwitzov teorem
• Kvaternioni i Frobeniusov teorem
• Paradoksalne dekompozicije
• Baireov teorem o kategoriji
• Hamelove baze i primjene
• Elementarni operatori na matricama (s M. Tomaševićem)

Skripte

• I. Gogić, Uvod u funkcionalnu analizu, skripta, PMF-MO, Zagreb
• I. Gogić, Diferencijalna geometrija, skripta, PMF-MO, Zagreb
• I. Gogić, P. Pandžić, J. Tambača, Diferencijalni račun funkcija više varijabli, skripta, PMF-MO, Zagreb
• I. Gogić, P. Pandžić, J. Tambača, Integrali funkcija više varijabli, skripta, PMF-MO, Zagreb
• I. Gogić, Odabrana poglavlja teorije operatorskih algebri, skripta, PMF-MO, Zagreb
• I. Gogić, A. Mimica, Matematička analiza 2, vježbe, PMF-MO, Zagreb

Stručni radovi

• I. Gogić, M. Bašić, D. Turčinović, J. Pucar Jambrović, Z. Pusić, Sjećanja na Senku Sedmak, Poučak: časopis za metodiku i nastavu matematike, Vol. 25 No. 97, 2024.
• I. Gogić, M. Tomašević, Gelfand-Mazurov teorem i Osnovni teorem algebre, časopis math.e, br. 37, 2020.

Mathematical links

• Functional Analysis Seminar in Zagreb
• Operator Algebra Searchable Information Site (OASIS)
• Operator Algebra page of N. C. Phillips
• Operator Algebra Resources
• Novi Sad Journal of Mathematics (NSJOM)
• Zagreb Workshop on Operator Theory 2020
• arXiv