Research

Research Framework

In the past 50 years, a major trend in Operator Theory focuses on the use of operator algebras for encoding geometrical and topological objects. Operator algebras may be considered as algebras of (bounded in norm) infinite matrices with complex entries. A central aspect of the program is to explore the passage from intrinsic properties of the object into properties of the associated operator algebras, and use invariants of the latter to classify the former. There are two interrelated questions that orient our study: 

Examples of examined objects so far include tilings, tangles, graphs, dynamical systems, groups, semigroups, varieties, homogeneous ideals, and stochastic matrices. My research so far incorporates operator algebras (both selfadjoint and non-selfadjoint) in terms of: representation theory, dilation theory, ideal structure, KMS-states theory, C*-envelopes, reflexivity, and hyperrigidity; for objects related to: C*-correspondences, product systems, subproduct systems, semigroup actions on operator algebras, and homogeneous ideals. 

Survey Papers, Conference Proceedings and Conference Reports

[3] Arici F, Kakariadis ETA, Larsen NS. Cuntz-Pimsner Cross-Pollination.
Nieuw Archief voor Wiskunde 5/20, Issue 1 (2019), 34-39.

[2] Davidson KR, Fuller AH, Kakariadis ETA. Semicrossed products of operator algebras: a survey.
New York Journal of Mathematics 24a (2018), 56-86.

[1] Kakariadis ETA, Katsoulis EG. Operator algebras and C*-correspondences: a survey.
Operator Theory: Advances and Applications 233 (2013), 45-73. 

Research Monographs

[1] Davidson KR, Fuller AH, Kakariadis ETA. Semicrossed products of operator algebras by semigroups.
Memoirs of the American Mathematical Society 247, no. 1168 (2017), (97 + v pages). 

Papers/Preprints in Pure Mathematics  

[33] Kakariadis ETA, Paraskevas IA. On Fock covariance and the reduced Hao-Ng isomorphism problem by discrete groups.
preprint (37 pages).

[32] Dessi J, Kakariadis ETA. Equivariant Nica-Pimsner quotients associated with strong compactly aligned product systems.
preprint (104 pages).

[31] Kakariadis ETA, Katoulis EG, Li X. Stable isomorphisms on operator algebras.
International Mathematics Research Notices (2023), rnad146, https://doi.org/10.1093/imrn/rnad146.

[30] Eleftherakis GK, Kakariadis ETA, Todorov IG. Morita equivalence for operator systems.
Journal d'Analyse Mathématique (32 pages).

[29] Kakariadis ETA, Katsoulis EG, Laca M, Li X. Co-universality and controlled maps on product systems over right LCM-semigroups.
Anaysis & PDE 16:6 (2023), 1433-1483.

[28] Kakariadis ETA, Katsoulis EG, Laca M, Li X. Boundary quotient C*-algebras of semigroups.
Journal of the London Mathematical Society 105:4 (2022), 2136-2166.

[27] Dor-On A, Kakariadis ETA, Katsoulis EG, Laca M, Li X. C*-envelopes for operator algebras with a coaction and co-universal C*-algebras for product systems.
Advances in Mathematics 400 (2022), 108286.

[26] Kakariadis ETA. Applications of entropy of product systems: higher-rank graphs.
Linear Algebra and its Applications 594 (2020), 124-157.

[25] Kakariadis ETA. Finite dimensional approximations for Nica-Pimsner algebras.
Ergodic Theory and Dynamical Systems 40:12 (2020), 3375-3402. 

[24] Kakariadis ETA, Katsoulis EG, Li X. Operator algebras of higher rank numerical semigroups.
Proceedings of the American Mathematical Society 148:10 (2020), 4423-4433.

[23] Kakariadis ETA. Equilibrium states and entropy theory for Nica-Pimsner algebras.
Advances in Mathematics 362 (2020), 106940, 59pp. 

[22] Dor-On A, Kakariadis ETA. Operator algebras for higher rank analysis and their application to factorial languages.
Journal d'Analyse Mathématique 143 (2021), 555--613.

[21] Kakariadis ETA. Entropy theory for the parametrization of the equilibrium states of Pimsner algebras.
 Journal of Geometry and Physics 155 (2020), 103794, 36pp.  

[20] Davidson KR, Kakariadis ETA. A proof of Boca's Theorem.
Proceedings of the Royal Society of Edinburgh Section A 149 (2019), 869-876.

[19] Bickerton RT, Kakariadis ETA. Free multivariate semicrossed products: reflexivity and the bicommutant property.
Canadian Journal of Mathematics 70:6 (2018), 1201-1235.

[18] Barrett C, Kakariadis ETA. On the quantized dynamics of factorial languages.
Quarterly Journal of Mathematics, 69:1 (2018), 119-152.
Program, Code, Code and Instructions for computing the Follower Set Graph of a Factorial Language on two symbols. The program was produced by Christopher Barrett during his MMath project. 

[17] Eleftherakis GK, Kakariadis ETA, Katsoulis EG. Morita equivalence of C*-correspondences passes to the related operator algebras.
Israel Journal of Mathematics 222:2 (2017), 949-972. 

[16] Eleftherakis GK, Kakariadis ETA. Strong Morita equivalence for operator spaces.
Journal of Mathematical Analysis and Applications 446:2 (2017), 1632-1653. 

[15] Kakariadis ETA, Shalit OM. On operator algebras associated with monomial ideals in noncommuting variables.
Journal of Mathematical Analysis and Applications 472:1 (2019), 738-813.  

[14] Kakariadis ETA. On Nica-Pimsner algebras of C*-dynamical systems over $\mathds{Z}_+^n$.
International Mathematics Research Notices 2017:4 (2017), 1013-1065. 

[13] Kakariadis ETA. KMS states on Pimsner algebras associated with C*-dynamical systems.
Journal of Functional Analysis 269:2 (2015), 325-354. 

[12] Kakariadis ETA, Peters JR. Ergodic extensions of endomorphisms.
Bulletin of the Australian Mathematical Society 93:2 (2016), 307-320. 

[11] Kakariadis ETA. A note on the gauge invariant uniqueness theorem for C*-correspondences.
Israel Journal of Mathematics 215:2 (2016), 513-521. 

[10] Kakariadis ETA. The Dirichlet property for tensor algebras.
Bulletin of the London Mathematical Society 45 (2013), 1119-1130. 

[9] Kakariadis ETA, Peters JR. Representations of C*-dynamical systems implemented by Cuntz families.
Münster Journal of Mathematics 6 (2013), 383-411. 

[8] Kakariadis ETA, Katsoulis EG. Isomorphisms invariants for multivariable C*-dynamics.
Journal of Noncommutative Geometry 8:3 (2014), 771-787. 

[7] Kakariadis ETA, Katsoulis EG. C*-algebras and equivalences for C*-correspondences.
Journal of Functional Analysis 266:2 (2014), 956-988.
Also see the Corrigendum to "C*-algebras and equivalences for C*-correspondences" that appeared at Journal of Functional Analysis 283:6 (2022), 109564. The proof of Theorem 5.8 gives a weaker version of shift equivalence than the one claimed in the statement. We show where the problem lies, adjust the main results --which are enough to tackle the two conjectures as they appear in the introduction-- and we make connections with results in the literature after the original paper appeared.

[6] Davidson KR, Kakariadis ETA. Conjugate dynamical systems on C*-algebras.
International Mathematics Research Notices 2014:5 (2014), 1289-1311. 

[5] Kakariadis ETA. The Silov boundary for operator spaces.
Integral Equations and Operator Theory 76:1 (2013), 25-38. 

[4] Kakariadis ETA. Semicrossed products of C*-algebras and their C*-envelopes.
Journal d'Analyse Mathématique 129:1 (2016), 1-31. 

[3] Kakariadis ETA, Katsoulis EG. Contributions to the theory of C*-correspondences with applications to multivariable dynamics.
Transactions of the American Mathematical Society 364:7 (2012), 6605-6630. 

[2] Kakariadis ETA, Katsoulis EG. Semicrossed products of operator algebras and their C*-envelopes.
Journal of Functional Analysis 262:7 (2012), 3108-3124. 

[1] Kakariadis ETA. Semicrossed products and reflexivity.
Journal of Operator Theory 67:2 (2012), 379-395.  

Papers in Healthcare

[1] Z. Tandogdu, E.T.A. Kakariadis, K. Naber, F.Wagenlehner, T.E.B. Johansen. Appropriate Empiric Antibiotic Choices in Health Care Associated Urinary Tract Infections in Urology Departments in Europe from 2006 to 2015: a Bayesian analytical approach applied in a surveillance study.
PLoS ONE 14(4): e0214710.

Notes

[4] Notes on Product systems and their representations: an approach using Fock spaces and Fell bundles, draft available upon request (preliminary version). 

[3] Notes on KMS-states of Pimsner algebras, for the 2019 Athens Minicourse (Erasmus+ Programme), draft available upon request. 

[2] Notes on C*-correspondences, draft available upon request. 

[1] Notes on The C*-envelope and the Silov Ideal. 

Theses

[T2] PhD Thesis: Operator Spaces and Operator Algebras: Semicrossed Products of Operator Algebras (in Greek).  

[T1] MSc Thesis: Wedderburn-type Structure Theorems in Topological Algebras (in Greek).