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Ali Jabbari

Publications and source records attributed to Ali Jabbari.

16 recordsLinked to original sources
arXiv2026

Functoriality and Weyl Groupoids of Ample C*-Diagonal Pairs

We develop a functorial framework for ample C$^*$-diagonal pairs and their Weyl groupoids. The main contribution is a partial functoriality theorem in the untwisted setting: from a diagonal-preserving $*$-homomorphism whose restriction to the diagonal is an isomorphism, we construct an open subgroupoid $\mathcal H_Φ\subseteq\mathcal G_B$ and a continuous, open, injective groupoid homomorphism $ρ_Φ: \mathcal H_Φ\to\mathcal G_A$, together with the induced homeomorphism on unit spaces. We prove that this construction is well-defined and extends to a contravariant functor into a category of partial groupoid morphisms, thereby giving a concrete partial Weyl-groupoid functor. We record consequences for expectation-compatible ideals, faithful conditional expectations, and quotient reductions, and formulate questions concerning the interaction with dynamical comparison. We also record tensor-product permanence results, including the product description of Weyl groupoids and the relevant diagonal-dimension estimate. Finally, in the untwisted principal case, we prove a reconstruction/rigidity theorem showing that the underlying Weyl groupoid determines the diagonal pair up to isomorphism. Results imported from Bönicke--Li, Li--Liao--Winter, Renault, Kumjian, and Kopsacheilis--Winter are used explicitly as background or supporting permanence results rather than claimed as new contributions.

math.OA↗
arXiv2026

A finitary criterion for selfless tracial C*-algebras

We study the class of selfless C*-probability spaces introduced by Robert. It is known that a selfless tracial algebra has strict comparison and a unique trace. We prove that for separable tracial C*-algebras, selflessness is equivalent to approximate selflessness, a finitary condition: for every finite set $F$, every $N \geq 1$ and $\varepsilon > 0$ there exists a unitary $u$ with $|τ(u^k)| < \varepsilon$ ($1 \leq |k| \leq N$) and $|τ(w)| < \varepsilon$ for all alternating words $w$ of length $\leq N$ built from centered elements of $F$ and powers $u^n$ ($|n| \leq N$). The equivalence is established using a diagonalisation argument in the tracial ultrapower. As an application, we give a concise proof that countable groups with a topologically-free extreme boundary are C*-selfless. We also discuss the relation to nuclearity and $\mathcal{Z}$-stability.

math.OA↗
arXiv2026

Breaking Status-Quo Inertia in Living Temporal Games: Dynamic Intervention, Implementation, and Structural Design

Westudy how a planner can design dynamic interventions to overcome status-quo inertia in living temporal games, where strategic agents control their state (active, sleep, partially dead) on a temporal network. Building on the continuous-time stochastic game framework of our companion paper, we introduce three intervention classes: bounded transfers (price based), structural modifications (edge deletion, addition, or replacement), and information signals. We formalize the notion of inertia depth and prove a threshold theorem: the status quo equilibrium survives all transfer perturbations whose magnitude is below a critical bound that depends on the remaining horizon. A central structural dominance result shows that for any finite transfer budget there exists a family of games where no bounded price intervention can eliminate the inefficient equilibrium, yet a single edge replacement (continuous-flow to discrete-transport) succeeds. We then study private-information subclasses with static types. Using a uniformization reduction, we prove an impossibility result: no direct mechanism can simultaneously satisfy ex post incentive compatibility, ex post budget balance, and history privacy while always implementing an efficient equilibrium. In the same subclass we construct a dynamic pivot mechanism that achieves second-best efficiency with bounded deficit. Finally, we show that replacing continuous-flow edges by discrete-transport edges weakly expands the set of implementable outcomes, highlighting the importance of temporal semantics for mechanism design. Our results extend the static analysis of [5] to continuous time strategic networks and provide a rigorous foundation for subsequent papers on learning and mean-field design.

econ.TH↗
arXiv2026

Amenability and Inner Amenability of Transformation Groups

In this paper, we show that there is a net for amenable transformation groups like Følner net for amenable groups and investigate amenability of a transformation group constructed by semidirect product of groups. We introduce inner amenability of transformation groups and characterize this property.

math.FA↗
arXiv2026

Quasi-isometric embedding between $*$-algebras

The concept of quasi-isometric embedding maps between $*$-algebras is introduced. We have obtained some basic results related to this notion and similar to quasi-isometric embedding maps on metric spaces, under some conditions, we give a necessary and sufficient condition on a $*$-homomorphism to be a quasi-isometric embedding between $*$-algebras.

math.FA↗
arXiv2022

Robust PCA for Anomaly Detection and Data Imputation in Seasonal Time Series

We propose a robust principal component analysis (RPCA) framework to recover low-rank and sparse matrices from temporal observations. We develop an online version of the batch temporal algorithm in order to process larger datasets or streaming data. We empirically compare the proposed approaches with different RPCA frameworks and show their effectiveness in practical situations.

stat.ML↗
arXiv2022

Some Results on Matricial Field C-Algebras

In this paper, we consider Blackadar and Kirchberg's MF algebras. We show that any inner quasidiagonal C-algebra is MF algebra and we generalize Voiculescu's Representation Theorem for a special version of MF algebras. Moreover, we define a weak version of MF algebras namely matrical amenable (AM) algebras, and prove some results related to this new notion. Finally, we consider real C-algebras and we show that a real C-algebra is MF if and only if its complexification is MF.

math.OA↗
arXiv2020

Cohomological properties and Arens regularity of Banach algebras

In this paper, we study some cohomlogical properties of Banach algebras. For a Banach algebra $A$ and a Banach $A$-bimodule $B$, we investigate the vanishing of the first Hochschild cohomology groups $H^1(A^n,B^m)$ and $H_{w^*}^1(A^n,B^m)$, where $0\leq m,n\leq 3$. For amenable Banach algebra $A$, we show that there are Banach $A$-bimodules $C$, $D$ and elements $\mathfrak{a}, \mathfrak{b}\in A^{**}$ such that $$Z^1(A,C^*)=\{R_{D^{\prime\prime}(\mathfrak{a})}:~D\in Z^1(A,C^*)\}=\{L_{D^{\prime\prime}(\mathfrak{b})}:~D\in Z^1(A,D^*)\}.$$ where, for every $b\in B$, $L_{b}(a)=ba$ and $R_{b}(a)=a b,$ for every $a\in A$. Moreover, under a condition, we show that if the second transpose of a continuous derivation from the Banach algebra $A$ into $A^*$ i.e., a continuous linear map from $A^{**}$ into $A^{***}$, is a derivation, then $A$ is Arens regular. Finally, we show that if $A$ is a dual left strongly irregular Banach algebra such that its second dual is amenable, then $A$ is reflexive.

math.FA↗
arXiv2020

Characterization of Symmetric Amenability of Unital Banach Algebras

In this paper, we introduce $p$-amenability, bounded $s$-symmetric approximate and $s$-symmetric virtual diagonals for a Banach algebra $\mathfrak{A}$ where $s$ is a non-zero element of algebraic center of $\mathfrak{A}$ that is denoted by $Z(\mathfrak{A})$. We show that if a Banach algebra $\mathfrak{A}$ is $p$-amenable then it has bounded $s$-symmetric approximate and $s$-symmetric virtual diagonals and by this fact we prove that if the Banach algebra $\mathfrak{A}$ is unital then $p$-amenability and symmetric amenability are equivalent.

math.FA↗
arXiv2020

A Weak Form of Amenability of Topological Semigroups and its Applications in Ergodic and Fixed Point Theories

In this paper, we introduce a weak form of amenability on topological semigroups that we call $φ$-amenability, where $φ$ is a character on a topological semigroup. Some basic properties of this new notion are obtained and by giving some examples, we show that this definition is weaker than the amenability of semigroups. As a noticeable result, for a topological semigroup $S$, it is shown that if $S$ is $φ$-amenable, then $S$ is amenable. Moreover, $φ$-ergodicity for a topological semigroup $S$ is introduced and it is proved that under some conditions on $S$ and a Banach space $X$, $φ$-amenability and $φ$-ergodicity of any antirepresntation defined by a right action $S$ on $X$, are equivalent. A relation between $φ$-amenability of topological semigroups and existance of a common fixed point is investigated and by this relation, Hahn-Banach property of topological semigroups in the sense of $φ$-amenability defined and studied.

math.FA↗
arXiv2015

Module Pseudo-amenability of Banach algebras

The notions of module pseudo-amenable and module pseudo-contractible Banach algebras are introduced. For a Banach algebra with bounded approximate identity, module pseudo-amenability and module approximate amenability are the same properties. It is given a complete characterization of module pseudo-amenability for a Banach algebra. For every inverse semigroup $S$ with subsemigroup $E$ of idempotents, necessary and sufficient conditions are obtained for the $\ell^1(S)$ and its second dual to be $\ell^1(E)$-module pseudo-amenable.

math.FA↗
arXiv2015

Module Biflatness of the second dual of Banach algebras

Let $\mathcal A$ be a Banach algebra. Using the concept of module biflatness, we show that the module amenability of the second dual $\mathcal A^{**}$ (with the first Arens product) necessitates the module amenability of $\mathcal A$. We give some examples of Banach algebras $\mathcal A$ such that $\mathcal A^{**}$ are module biflat, but which are not themselves module biflat.

math.FA↗
arXiv2013

n-Weak Module Amenability of Triangular Banach Algebras

Let $\mathcal A$, $\mathcal B$ be Banach $\mathfrak A$-modules with compatible actions and $\mathcal M$ be a left Banach $\mathcal A$-$\mathfrak A$-module and a right Banach $\mathcal B$-$\mathfrak A$-module. In the current paper, we study module amenability, $n$-weak module amenability and module Arens regularity of the triangular Banach algebra $\mathcal T=[ {cc} \mathcal A & \mathcal M & \mathcal B ]$ (as an $\mathfrak T:=\Big{[ {cc} α& & α ] | α\in\mathfrak A\Big}$-module). We employ these results to prove that for an inverse semigroup $S$ with subsemigroup $E$ of idempotents, the triangular Banach algebra $\mathcal T_0=[ {cc} \ell^1(S)& \ell^1(S) & \ell^1(S) ]$ is permanently weakly module amenable (as an $\mathfrak T_0=[ {cc} \ell^1(E)& & \ell^1(E) ]$-module). As an example, we show that $\mathcal T_0$ is $\mathfrak T_0$-module Arens regular if and only if the maximal group homomorphic image $G_S$ of $S$ is finite.

math.FA↗