Searcharxiv⌕ Search

arXiv subjects

Minghui Ma

Publications and source records attributed to Minghui Ma.

At least 19 recordsLinked to original sources
arXiv2026

Kaplansky's second test problem in operator algebras

Kaplansky's second test problem on similarity asks: if $T$ and $S$ are elements in a unital Banach algebra $\mathcal{B}$ and $T\oplus T$ is similar to $S\oplus S$ in $\mathbb{M}_2(\mathcal{B})$, is $T$ similar to $S$ in $\mathcal{B}$? We answer this problem affirmatively if $T$ is an operator with property $(J)$ in a type $\mathrm{I}_n$ von Neumann algebra $\mathcal{M}$, i.e., $\{T\}'\cap\mathcal{M}$ contains a bounded maximal abelian family of idempotents. Moreover, the condition of property $(J)$ can be removed for $1\leqslant n\leqslant 3$. A similar result is proved if $T$ is an element in a unital Banach algebra $\mathcal{B}$ with essentially finite-dimensional commutant, i.e., the relative commutant of $T$ in $\mathcal{B}$ is finite-dimensional modulo its Jacobson radical. Finally, we point out that one of our main results can be applied to the implementation of local unitary (LU) equivalence of quantum states.

math.FA↗
arXiv2026

Bargmann invariants and local unitary equivalence

In this paper, we study the local unitary equivalence of quantum states on $\mathbb{C}^n\otimes\mathbb{C}^n$, which is an important notion in quantum information theory. For the case $n=2$, the local unitary orbits of two-qubit states are completely determined by their local unitary Bargmann invariants. We show that the local unitary Bargmann invariants do not form a complete set of invariants of local unitary orbits for $n\geqslant 3$, which negatively answers a problem proposed by L. Zhang and B. Xie.

quant-ph↗
arXiv2026

Cognitive World Model for Progressive BDI/E Trajectory Evaluation of Conversational Agents

As LLM-based conversational agents advance toward increasingly open-ended and interaction-intensive scenarios, task completion alone provides an incomplete assessment of their effectiveness. The evolution of users' internal states, including beliefs, desires, intentions, and emotions (BDI/E), serves as an intermediate signal connecting agent behaviors with interaction outcomes and reflects how conversational strategies shape users during multi-turn interactions. However, existing evaluation paradigms primarily focus on surface-level responses or final outcomes, providing limited insight into the underlying cognitive processes. This limitation makes it difficult to diagnose why agents succeed or fail and to optimize their interaction strategies. To address this challenge, we propose Cognitive World Model (CogWM), an LLM-based cognitive user model that jointly models users' BDI/E states and corresponding responses, enabling explicit cognitive trajectory tracking. Trained on 150K user-turn samples with Qwen3-14B, CogWM achieves superior performance over existing user simulation baselines in both response fidelity and cognitive state understanding. Interactions with six state-of-the-art LLMs demonstrate that CogWM enables progressive comparison of agents through cognitive trajectories, revealing distinct agent patterns and complementary relationships between cognitive evolution and behavioral outcomes.

cs.AI↗
arXiv2026

Think Thrice Before You Speak: Dual knowledge-enhanced Theory-of-Mind Reasoning for Persuasive Agents

Persuasive dialogue requires reasoning about others' latent mental states, a capability known as Theory of Mind (ToM). However, due to reliance on simple prompting strategies and insufficient ToM knowledge, existing LLMs often fail to capture the intrinsic dependencies among mental states, leading to fragmented representations and unstable reasoning. To address these challenges, we introduce the ToM-based Persuasive Dialogue (ToM-PD) task, grounded in the Belief-Desire-Intention (BDI) framework, which explicitly models the sequential dependencies among mental states in multi-turn dialogues. To facilitate research on this task, we construct a large-scale annotated dataset, ToM-based Broad Persuasive Dialogues (ToM-BPD), capturing fine-grained mental states and corresponding persuasive strategies. We further propose Think Thrice Before You Speak (TTBYS), a knowledge-enhanced stepwise reasoning framework that leverages both explicit and implicit prior experiences to improve LLMs' inference of desires, beliefs, and persuasive strategies. Experimental results demonstrate that Qwen3-8B equipped with TTBYS outperforms GPT-5 by 1.20%, 22.80%, and 16.97% in predicting desires, beliefs, and persuasive strategies, respectively. Case studies further show that our approach enhances interpretability and consistency in reasoning.

cs.AI↗
arXiv2026

The similarity of irreducible operators in factors

An operator $T$ in a separable factor $\mathcal{M}$ is said to be irreducible in $\mathcal{M}$ if the von Neumann subalgebra $W^*(T)$ generated by $T$ is an irreducible subfactor of $\mathcal{M}$, i.e., $W^*(T)'\cap\mathcal{M}=\mathbb{C}I$. We say that $T$ is a single generator of $\mathcal{M}$ if $W^*(T)=\mathcal{M}$. In this paper, we study generators of separable factors related to maximal abelian self-adjoint subalgebras. As an application, we obtain a complete characterization of normal operators in separable factors which are similar to irreducible operators.

math.OA↗
arXiv2026

Operators with disconnected spectrum in von Neumann algebras

Let $\mathcal{M}$ be a von Neumann algebra, $\mathcal{I}$ a weak-operator dense ideal in $\mathcal{M}$, and $\Phi$ a unitarily invariant $\|\cdot\|$-dominating norm on $\mathcal{I}$. In this paper, we provide a necessary and sufficient condition on $\Phi$ such that every operator in $\mathcal{M}$ can be expressed as the sum of an operator in $\mathcal{M}$ with disconnected spectrum and an operator in $\mathcal{I}$ whose $\Phi$-norm is arbitrarily small. Similarly, if $\mathcal{A}$ is a unital $C^*$-algebra of real rank zero with dimension greater than one and $\mathcal{I}$ is an essential ideal in $\mathcal{A}$, then every element in $\mathcal{A}$ can be written as the sum of an operator in $\mathcal{A}$ with disconnected spectrum and an operator in $\mathcal{I}$ whose norm is arbitrarily small.

math.OA↗
arXiv2025

Products of irreducible operators in factors

Let $\mathcal M$ be a separable factor. An operator $T$ in $\mathcal{M}$ is said to be irreducible in $\mathcal{M}$ if the von Neumann algebra $W^*(T)$ generated by $T$ is an irreducible subfactor of $\mathcal{M}$, i.e., $W^*(T)'\cap\mathcal{M}=\mathbb{C}I$. In this paper, we show that every operator in a separable factor $\mathcal{M}$ is the product of two irreducible operators in $\mathcal{M}$, except the zero operator in factors of type $\mathrm{I}_{2n+1}$ for $n\geqslant 1$. This may be viewed as a multiplicative analogue of Radjavi's result which asserts that every operator on a separable Hilbert space is the sum of two irreducible operators.

math.OA↗
arXiv2025

Irreducible operators in von Neumann algebras

Let $\mathcal{M}$ be a separable von Neumann algebra with center $\mathcal{Z}(\mathcal{M})$. An operator $T$ in $\mathcal{M}$ is called irreducible if the von Neumann algebra $W^*(T)$ generated by $T$ has trivial relative commutant, i.e., $W^*(T)'\cap\mathcal{M}=\mathcal{Z}(\mathcal{M})$. In this paper, we show that irreducible operators in $\mathcal{M}$ form a norm-dense $G_\delta$ set, which is a generalization of Halmos' theorem. Moreover, we prove that every operator in $\mathcal{M}$ is the sum of two irreducible operators, which is an analogue of Radjavi's theorem.

math.OA↗
arXiv2025

Ortho-isomorphisms of von Neumann algebras

Suppose $\mathscr M$ and $\mathscr N$ are von Neumann algebras. Two operators $A$ and $B$ in $\mathscr M$ are said to be orthogonal if $A^*B=0$, meaning their ranges are orthogonal. Let $\varphi\colon\mathscr M\to\mathscr N$ be a map. We say that $\varphi$ is an ortho-isomorphism if it is bijective and satisfies that $A^*B=0$ if and only if $\varphi(A)^*\varphi(B)=0$ for all $A,B\in\mathscr M$. The map $\varphi$ is called ortho-additive if the additive relation $\varphi(A+B)=\varphi(A)+\varphi(B)$ holds for all $A,B\in \mathscr M$ with $A^*B=0$. In this paper, we characterize the complete structure of ortho-additive ortho-isomorphisms between von Neumann algebras, which is an analogue of Dye's theorem and Uhlhorn's theorem.

math.OA↗
arXiv2025

Free semigroupoid algebras and the first cohomology groups

This paper investigates derivations of the free semigroupoid algebra $\mathfrak{L}_G$ of a countable or uncountable directed graph $G$ and its norm-closed version, the tensor algebra $\mathcal{A}_G$. We first prove a weak Dixmier approximation theorem for $\mathfrak{L}_G$ when $G$ is strongly connected. Using the theorem, we show that if every connected component of $G$ is strongly connected, then every bounded derivation $\delta$ from $\mathcal{A}_G$ into $\mathfrak{L}_G$ is of the form $\delta=\delta_T$ for some $T\in\mathfrak{L}_G$ with $\|T\|\leqslant\|\delta\|$. For any finite directed graph $G$, we also show that the first cohomology group $H^1(\mathcal{A}_G,\mathfrak{L}_G)$ vanishes if and only if every connected component of $G$ is either strongly connected or a fruit tree. To handle infinite directed graphs, we introduce the alternating number and propose \Cref{conj intro-in-tree}. Suppose every connected component of $G$ is not strongly connected. We show that if every bounded derivation from $\mathcal{A}_G$ into $\mathfrak{L}_G$ is inner, then every connected component of $G$ is a generalized fruit tree and the alternating number $A(G)$ of $G$ is finite. The converse is also true if the conjecture holds. Finally, we provide some examples of free semigroupoid algebras together with their nontrivial first cohomology groups.

math.OA↗
arXiv2025

Density of irreducible operators in the trace-class norm

In 1968, Paul Halmos initiated the research on density of the set of irreducible operators on a separable Hilbert space. Through the research, a long-standing unsolved problem inquires: is the set of irreducible operators dense in $B(H)$ with respect to the trace-class norm topology? Precisely, for each operator $T $ in $B(H)$ and every $\varepsilon >0$, is there a trace-class operator $K$ such that $T+K$ is irreducible and $\Vert K \Vert_1 < \varepsilon$? For $p>1$, to prove the $\Vert \cdot \Vert_p$-norm density of irreducible operators in $B(H)$, a type of Weyl-von Neumann theorem effects as a key technique. But the traditional method fails for the case $p=1$, where by $\Vert \cdot \Vert_p$-norm we denote the Schatten $p$-norm. In the current paper, for a large family of operators in $B(H)$, we give the above long-term problem an affirmative answer. The result is derived from a combination of techniques in both operator theory and operator algebras. Moreover, we discover that there is a strong connection between the problem and another related operator-theoretical problem related to type $\mathrm{II}_1$ von Neumann algebras.

math.OA↗
arXiv2025

On cleanness of AW*-algebras

A ring is called clean if every element is the sum of an invertible element and an idempotent. This paper investigates the cleanness of AW*-algebras. We prove that all finite AW*-algebras are clean, affirmatively solving a question posed by Vas. We also prove that all countably decomposable infinite AW*-factors are clean. A *-ring is called almost *-clean if every element can be expressed as the sum of a non-zero-divisor and a projection. We show that an AW*-algebra is almost *-clean if and only if it is finite.

math.OA↗
arXiv2024

Hochschild cohomology for free semigroup algebras

This paper focuses on the cohomology of operator algebras associated with the free semigroup generated by the set $\{z_{\alpha}\}_{\alpha\in\Lambda}$, with the left regular free semigroup algebra $\mathfrak{L}_{\Lambda}$ and the non-commutative disc algebra $\mathfrak{A}_{\Lambda}$ serving as two typical examples. We establish that all derivations of these algebras are automatically continuous. By introducing a novel computational approach, we demonstrate that the first Hochschild cohomology group of $\mathfrak{A}_{\Lambda}$ with coefficients in $\mathfrak{L}_{\Lambda}$ is zero. Utilizing the Ces\`aro operators and conditional expectations, we show that the first normal cohomology group of $\mathfrak{L}_{\Lambda}$ is trivial. Finally, we prove that the higher cohomology groups of the non-commutative disc algebras with coefficients in the complex field vanish when $|\Lambda|<\infty$. These methods extend to compute the cohomology groups of a specific class of operator algebras generated by the left regular representations of cancellative semigroups, which notably include Thompson's semigroup.

math.OA↗
arXiv2024

Research on signalized intersection mixed traffic flow platoon control method considering Backward-looking effect

Connected and Autonomous Vehicles (CAVs) technology facilitates the advancement of intelligent transportation. However, intelligent control techniques for mixed traffic flow at signalized intersections involving both CAVs and Human-Driven Vehicles (HDVs) require further investigation into the impact of backward-looking effect. This paper proposes the concept of 1+n+1 mixed platoon considering the backward-looking effect, consisting of one leading CAV, n following HDVs, and one trailing CAV. The leading and trailing CAVs collectively guide the movement of intermediate HDVs at intersections, forming an optimal control framework for platoon-based CAVs at signalized intersections. Initially, a linearized dynamic model for the 1+n+1 mixed platoon is established and compared with a benchmark model focusing solely on controlling the lead vehicle. Subsequently, constraints are formulated for the optimal control framework, aiming to enhance overall intersection traffic efficiency and fuel economy by directly controlling the leading and trailing CAVs in the platoon. Finally, extensive numerical simulations compare vehicle throughput and fuel consumption at signalized intersections under different mixed platoon control methods, validating that considering both front and backward-looking effects in the mixed platoon control method outperforms traditional methods focusing solely on the lead CAV.

physics.app-ph↗
arXiv2024

Voiculescu's Theorem in Properly Infinite Factors

In this paper, we investigate Voiculescu's theorem on approximate unitary equivalence in separable properly infinite factors. As applications, we establish the norm-denseness of the set of all reducible operators, prove a generalized Voiculescu's bicommutant theorem and a version of asymptotic bicommutant theorem, and obtain an interesting cohomological result. Additionally, we extend these results to multiplier algebras within separable type $\mathrm{III}$ factors. At last, a concept of the nuclear length is introduced.

math.OA↗
arXiv2019

The Finite Model Property of Quasi-transitive Modal Logic

The finite model property of quasi-transitive modal logic $\mathsf{K}_2^3=\mathsf{K}\oplus \Box\Box p\rightarrow \Box\Box\Box p$ is established. This modal logic is conservatively extended to the tense logic $\mathsf{Kt}_2^3$. We present a Gentzen sequent calculus $\mathsf{G}$ for $\mathsf{Kt}_2^3$. The sequent calculus $\mathsf{G}$ has the finite algebra property by a finite syntactic construction. It follows that $\mathsf{Kt}_2^3$ and $\mathsf{K}_2^3$ have the finite model property.

cs.LO↗
arXiv2017

Graphical Sequent Calculi for Modal Logics

The syntax of modal graphs is defined in terms of the continuous cut and broken cut following Charles Peirce's notation in the gamma part of his graphical logic of existential graphs. Graphical calculi for normal modal logics are developed based on a reformulation of the graphical calculus for classical propositional logic. These graphical calculi are of the nature of deep inference. The relationship between graphical calculi and sequent calculi for modal logics is shown by translations between graphs and modal formulas.

cs.LO↗