Eusebio Gardella

activity

20142026

L^{p}

-spaces

34 citations · 176 across the 46 of their papers we have counts for

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40 papers · 1 filter

math.OA2026

Classifiability of crossed products

Eusebio Gardella

This survey studies C*-algebraic crossed products arising from topological dynamical systems with an eye toward their classifiability in the sense of the Elliott program. We introd…

math.OA2025

Topological full groups, invertible isometries, and automorphisms of groupoid algebras

Eusebio Gardella, Mathias Palmstrøm, Hannes Thiel

We show that the topological full group of a Hausdorff ample groupoid with compact unit space coincides with the group of homotopy classes of invertible isometries in pseudofunctio…

math.OA2025

Rigidity of pseudofunction algebras of ample groupoids

Eusebio Gardella, Mathias Palmstrøm, Hannes Thiel

We show that a Hausdorff, ample groupoid $G$ can be completely recovered from the $I$ -norm completion of $C_{c} (G)$ . More generally, we show that this is also the…

math.OA2025

Prime and semiprime Lie ideals in C*-algebras

Eusebio Gardella, Kan Kitamura, Hannes Thiel

Using the theory of Dixmier ideals developed in previous work, we show that every semiprime Lie ideal in a C*-algebra arises as the full normalizer subspace of a semiprime two-side…

math.OA2025

Simplicity of $C^{*}$ -algebras of contracting self-similar groups

Eusebio Gardella, Volodymyr Nekrashevych, Benjamin Steinberg +1

We show that the $C^{*}$ -algebra associated by Nekrashevych to a contracting self-similar group is simple if and only if the corresponding complex $*$ -algebra is simple. We also i…

math.OA2024

Essential freeness, allostery and $Z$ -stability of crossed products

Eusebio Gardella, Shirly Geffen, Rafaela Gesing +2

We explore classifiability of crossed products of actions of countable amenable groups on compact, metrizable spaces. It is completely understood when such crossed products are sim…

math.OA2024

Actions on classifiable C*-algebras without equivariant property (SI)

Eusebio Gardella, Julian Kranz, Andrea Vaccaro

We exhibit examples of actions of countable discrete groups on both simple and non-simple nuclear stably finite C*-algebras that are tracially amenable but not amenable. We further…

math.OA2023

Semiprime ideals in C*-algebras

Eusebio Gardella, Kan Kitamura, Hannes Thiel

We show that a not necessarily closed ideal in a C*-algebra is semiprime if and only if it is idempotent, if and only if it is closed under square roots of positive elements. Among…

math.OA2023

Prime ideals in C*-algebras and applications to Lie theory

Eusebio Gardella, Hannes Thiel

We show that every proper, dense ideal in a C*-algebra is contained in a prime ideal. It follows that a subset generates a C*-algebra as a not necessarily closed ideal if and only…

math.OA2022★ 1 cited

The modern theory of Cuntz semigroups of C*-algebras

Eusebio Gardella, Francesc Perera

We give a detailed introduction to the theory of Cuntz semigroups for C*-algebras. Beginning with the most basic definitions and technical lemmas, we present several results of his…

math.OA2022★ 1 cited

Tracially amenable actions and purely infinite crossed products

Eusebio Gardella, Shirly Geffen, Julian Kranz +2

We introduce the notion of tracial amenability for actions of discrete groups on unital, tracial C $^{*}$ -algebras, as a weakening of amenability where all the relevant approximations…

math.OA2022

Dynamical comparison and $Z$ -stability for crossed products of simple $C^{*}$ -algebras

Eusebio Gardella, Shirly Geffen, Petr Naryshkin +1

We establish $Z$ -stability for crossed products of outer actions of amenable groups on $Z$ -stable $C^{*}$ -algebras under a mild technical assumption which we call…

math.OA2022

Weighted homomorphisms between C*-algebras

Eusebio Gardella, Hannes Thiel

We show that a bounded, linear map between C*-algebras is a weighted $*$ -homomorphism (the central compression of a $*$ -homomorphism) if and only if it preserves zero-product…

math.OA2022★ 1 cited

Classifiability of crossed products by nonamenable groups

Eusebio Gardella, Shirly Geffen, Julian Kranz +1

We show that all amenable, minimal actions of a large class of nonamenable countable groups on compact metric spaces have dynamical comparison. This class includes all nonamenable…

math.OA2021★ 3 cited

Strongly outer actions of amenable groups on $Z$ -stable nuclear $C^{*}$ -algebras

Eusebio Gardella, Ilan Hirshberg, Andrea Vaccaro

Let $A$ be a separable, unital, simple, $Z$ -stable, nuclear $C^{*}$ -algebra, and let $α : G \to Aut (A)$ be an action of a discrete, countable, amenable group. S…

math.OA2021

Equivariant bundles and absorption

Marzieh Forough, Eusebio Gardella

For a locally compact group $G$ and a strongly self-absorbing $G$ -algebra $(D, δ)$ , we obtain a new characterization of absorption of a strongly self-absorbing action usin…

math.OA2021

Asymptotic lifting for completely positive maps

Marzieh Forough, Eusebio Gardella, Klaus Thomsen

Let $A$ and $B$ be $C^{*}$ -algebras with $A$ separable, let $I$ be an ideal in $B$ , and let $ψ : A \to B / I$ be a completely positive contractive linear map. We show that there is…

math.OA2020

Partial C*-dynamics and Rokhlin dimension

Fernando Abadie, Eusebio Gardella, Shirly Geffen

We develop the notion of Rokhlin dimension for partial actions of finite groups, extending the well-established theory for global systems. The partial setting exhibits phenomena th…

math.OA2020★ 3 cited

Decomposable partial actions

Fernando Abadie, Eusebio Gardella, Shirly Geffen

We define the decomposition property for partial actions of discrete groups on $C^{*}$ -algebras. Decomposable partial systems appear naturally in practice, and many commonly occurrin…

math.OA2019★ 12 cited

Rigidity results for $L^{p}$ -operator algebras and applications

Yemon Choi, Eusebio Gardella, Hannes Thiel

For $p \in [1, \infty)$ , we show that every unital $L^{p}$ -operator algebra contains a unique maximal $C^{*}$ -subalgebra, which is always abelian if $p \neq = 2$ . Using this, we canonically…

math.OA2018★ 3 cited

Strongly outer actions of amenable groups on $Z$ -stable $C^{*}$ -algebras

Eusebio Gardella, Ilan Hirshberg

Let $A$ be a separable, unital, simple, $Z$ -stable, nuclear $C^{*}$ -algebra, and let $α : G \to Aut (A)$ be an action of a countable amenable group $G$ . If the t…

math.OA2018

Actions of nonamenable groups on $Z$ -stable $C^{*}$ -algebras

Eusebio Gardella, Martino Lupini

We study strongly outer actions of discrete groups on C*-algebras in relation to (non)amenability. In contrast to related results for amenable groups, where uniqueness of strongly…

math.OA2018

Compact group actions with the Rokhlin property

Eusebio Gardella

We provide a systematic and in-depth study of compact group actions with the Rokhlin property. It is show that the Rokhlin property is generic in some cases of interest; the case o…

math.OA2018★ 2 cited

The local-triviality dimension of actions of compact quantum groups

Eusebio Gardella, Piotr M. Hajac, Mariusz Tobolski +1

We define the local-triviality dimension for actions of compact quantum groups on unital C*-algebras. The resulting compact quantum principal bundle is said to be locally trivial w…

Classifiability of crossed products

Topological full groups, invertible isometries, and automorphisms of groupoid algebras

Rigidity of pseudofunction algebras of ample groupoids

Prime and semiprime Lie ideals in C*-algebras

Simplicity of C∗-algebras of contracting self-similar groups

Essential freeness, allostery and Z-stability of crossed products

Actions on classifiable C*-algebras without equivariant property (SI)

Semiprime ideals in C*-algebras

Prime ideals in C*-algebras and applications to Lie theory

The modern theory of Cuntz semigroups of C*-algebras

Tracially amenable actions and purely infinite crossed products

Dynamical comparison and Z-stability for crossed products of simple C∗-algebras

Weighted homomorphisms between C*-algebras

Classifiability of crossed products by nonamenable groups

Strongly outer actions of amenable groups on Z-stable nuclear C∗-algebras

Equivariant bundles and absorption

Asymptotic lifting for completely positive maps

Partial C*-dynamics and Rokhlin dimension

Decomposable partial actions

Rigidity results for Lp-operator algebras and applications

Strongly outer actions of amenable groups on Z-stable C∗-algebras

Actions of nonamenable groups on Z-stable C∗-algebras

Compact group actions with the Rokhlin property

The local-triviality dimension of actions of compact quantum groups

Simplicity of $C^{*}$ -algebras of contracting self-similar groups

Essential freeness, allostery and $Z$ -stability of crossed products

Dynamical comparison and $Z$ -stability for crossed products of simple $C^{*}$ -algebras

Strongly outer actions of amenable groups on $Z$ -stable nuclear $C^{*}$ -algebras

Rigidity results for $L^{p}$ -operator algebras and applications

Strongly outer actions of amenable groups on $Z$ -stable $C^{*}$ -algebras

Actions of nonamenable groups on $Z$ -stable $C^{*}$ -algebras