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Research

My main research interests are in operator algebras, noncommutative dynamics, abstract harmonic analysis, and operators on L^p spaces. Most of my work is related to at least one of the following:

  • Connections between amenability of a discrete group and actions on C*-algebras.
  • Classification and internal structure of group actions and their crossed products.
  • The interactions of model theory and descriptive set theory with Functional Analysis.
  • Group representations on Banach spaces, particularly on L^p spaces.

    • Publications

    (See also my MathSciNet and zbMATH entries.)
    1. E. Gardella, S. Geffen, J. Kranz, P. Naryshkin, A. Vaccaro, "Tracial amenability and purely infinite crossed products". Math. Ann., to appear (2024). DOI: 10.1007/s00208-024-02833-9.
    2. E. Gardella, H. Thiel, "Prime ideals in C*-algebras and applications to Lie theory". Proc. Amer. Math. Soc., to appear (2024). Arxiv preprint math.OA/2306.2306.16510.
    3. E. Gardella, S. Geffen, P. Naryshkin, A. Vaccaro, "Dynamical comparison and Z-stability for crossed products of simple C*-algebras". Adv. Math. 438 (2024), 109471.
    4. E. Gardella, H. Thiel, "Zero-product balanced algebras". Linear Algebra Appl. 670 (2023), no. 1, 121--153.
    5. E. Gardella, S. Geffen, J. Kranz, P. Naryshkin, "Classifiability of crossed products by nonamenable groups ". J. Reine Angew. Math. 797 (2023), 285--312.
    6. E. Gardella, I. Hirshberg, A. Vaccaro, "Strongly outer actions of amenable groups on Z-stable nuclear C*-algebras". J. Math. Pures Appl. 162 (2022), 76--123.
    7. E. Gardella, H. Thiel, "Isomorphisms of algebras of convolution operators". Ann. Sci. École Nor. Sup. (4) 55 (2022), no. 5, 1433--1471.
    8. E. Gardella, "Equivariant KK-theory and the continuous Rokhlin property". Int. Math. Res. Not. IMRN (2022), no. 21, 16779--16813.
    9. F. Abadie, E. Gardella, S. Geffen, "Partial C*-dynamics and Rokhlin dimension". Ergodic Theory Dynam. Syst. 42 (2022), 2991--3024.
    10. E. Gardella, M. Lupini, "Group amenability and actions on Z-stable C*-algebras". Adv. Math. 389 (2021), 107931.
    11. E. Gardella, "A modern look to algebras of operators on Lp-spaces". Expo. Math. 39 (2021), no. 3, 420--453.
    12. F. Abadie, E. Gardella, S. Geffen, "Decomposable partial actions". J. Funct. Anal. 281 (2021), no. 7, 109112.
    13. E. Gardella, I. Hirshberg, L. Santiago, "Rokhlin dimension: duality, tracial properties, and crossed products". Ergodic Theory Dynam. Syst. 41 (2021), no. 2, 408--460.
    14. E. Gardella, H. Thiel, "Preduals and complementation of spaces of bounded linear operators". Internat. J. Math. 31 (2020), no. 7, 2050053, 26 pp.
    15. E. Gardella, H. Thiel, "Extending representations of Banach algebras to their biduals". Math. Z. 294 (2020), no. 3-4, 1341--1354.
    16. E. Gardella, M. Kalantar, M. Lupini, "Rokhlin dimension for compact quantum group actions". J. Noncommut. Geom. 13 (2019), no. 2, 711--767.
    17. E. Gardella, H. Thiel, "Representations of p-convolution algebras on Lq-spaces". Trans. Amer. Math. Soc 371 (2019), no. 3, 2207--2236.
    18. E. Gardella, "Amenability, group actions, and orbit equivalence". Publ. Mat. Urug. 17 (2019), no. 1, 141--152.
    19. E. Gardella, "Compact group actions with the Rokhlin property". Trans. Amer. Math. Soc. 371 (2019), no. 4, 2837--2874.
    20. E. Gardella, M. Lupini, "Actions of rigid groups on UHF-algebras". J. Funct. Anal. 275 (2018), no. 2, 381--421.
    21. E. Gardella, "Circle actions on UHF-absorbing C*-algebras". Houston J. Math. 44 (2018), no. 2, 571--601.
    22. E. Gardella, M. Lupini, "Applications of model theory to C*-dynamics". J. Funct. Anal. 275 (2018), no. 3-4, 1341--1354.
    23. E. Gardella, "Crossed products by compact group actions with the Rokhlin property.". J. Noncomm. Geom. 11 (2017), no. 4, 1593--1626.
    24. E. Gardella, M. Lupini, "On the classification problem of free ergodic actions of nonamenable groups". C. R. Math. Acad. Sci. Paris 355 (2017), no. 10, 1037--1040.
    25. E. Gardella, M. Lupini, "Representations of étale groupoids on Lp-spaces". Adv. Math. 318 (2017), 233--278.
    26. E. Gardella, L. Santiago, "The equivariant Cuntz semigroup". Proc. Lond. Math. Soc. (3) 114 (2017), no. 2, 189--241.
    27. E. Gardella, "Rokhlin dimension for compact group actions". Indiana U. Math. J. 66 (2017), 659--703.
    28. E. Gardella, "Regularity properties and Rokhlin dimension for compact group actions". Houston J. Math. 43 (2017), no. 3, 861--889.
    29. E. Gardella, H. Thiel, "Quotients of Banach algebras acting on Lp-spaces". Adv. Math. 296 (2016), 85--92.
    30. E. Gardella, M. Lupini, "Conjugacy and cocycle conjugacy of automorphisms of O_2 are not Borel". Münster J. of Math. 9 (2016), 93--118.
    31. E. Gardella, M. Lupini, "Nonclassifiability of UHF Lp-operator algebras". Proc. Amer. Math. Soc. 144 (2016), no. 5, 2081--2091.
    32. E. Gardella, L. Santiago, "Equivariant *-homomorphisms, Rokhlin constraints and equivariant UHF-absorption". J. Funct. Anal. 270 (2016), no. 7, 2543--2590.
    33. E. Gardella, H. Thiel, "Group algebras acting on Lp-spaces". J. Fourier Anal. Appl. 21 (2015), no. 6, 1310--1343.
    34. E. Gardella, H. Thiel, "Banach algebras generated by an invertible isometry of an Lp-space". J. Funct. Anal. 269 (2015), no. 6, 1796--1839.

    Preprints

    (I post my preprints on the arXiv.)
    1. E. Gardella, J. Kranz, A. Vaccaro, "Actions on classifiable C*-algebras without equivariant property (SI)". Arxiv preprint math.OA/2402.16637, 2024.
    2. E. Gardella, K. Kitamura, H. Thiel, "Semiprime ideals in C*-algebras". Arxiv preprint math.OA/2311.17480, 2023.
    3. E. Gardella, O. Tanner, "Generalisations of Thompson's group V arising from purely infinite groupoids". Arxiv preprint math.GR/2302.04078, 2023.
    4. E. Gardella, H. Thiel, "Rings and C*-algebras generated by commutators". Arxiv preprint math.RA/2301.05958, 2023.
    5. E. Gardella, F. Perera, "The modern theory of Cuntz semigroups of C*-algebras". Arxiv math.OA/2212.02290, 2022.
    6. E. Gardella, H. Thiel, "Weighted homomorphisms between C*-algebras". Arxiv preprint math.OA/2203.16702, 2022.
    7. M. Forough, E. Gardella, "Equivariant bundles and absorption". Arxiv preprint math.OA/2104.14927, 2021.
    8. M. Forough, E. Gardella, K. Thomsen, "Asymptoting lifting for completely positive maps". Arxiv preprint math.OA/2103.09176, 2021.
    9. Y. Choi, E. Gardella, H. Thiel, "Rigidity results for Lp-operator algebras and applications". Arxiv preprint math.OA/1909.03612, 2019.
    10. E. Gardella, I. Hirshberg, "Strongly outer actions of amenable groups on Z-stable C*-algebras". Arxiv preprint math.OA/1811.00447, 2018.
    11. E. Gardella, P. Hajac, M. Tobolski, J. Wu, "The local-triviality dimension of actions of compact quantum groups". Arxiv preprint math.OA/1801.00767, 2018.
    12. E. Gardella, N. C. Phillips, Q. Wang, "Absorption of model actions on the Jiang-Su algebra". Preprint available here, 2017.
    13. E. Gardella, M. Lupini, "The Borel complexity of conjugacy, orbit equivalence, and von Neumann equivalence of actions of nonamenable groups". Arxiv preprint math.DS/1708.01327, 2017.
    14. E. Gardella, H. Thiel, "Functoriality of group algebras acting on Lp-spaces". Arxiv preprint math.OA/1408.6137, 2014.
    15. E. Gardella, "Classification theorems for circle actions on Kirchberg algebras, I". Arxiv preprint math.OA/1405.2469, 2014.