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Jinghao Huang

Publications and source records attributed to Jinghao Huang.

At least 37 records · Page 2Linked to original sources
arXiv2026

Disjointness-preserving mappings on Calkin operator spaces and positive isometries

Let $E(\mathcal{M},τ)$ and $F(\mathcal{M},τ)$ be two Calkin operator spaces affiliated with a semifinite von Neumann algebra $\mathcal{M}$ equipped with a semifinite faithful normal trace $τ$. We show that if $\mathcal{M}$ is atomless, $τ$ is finite, and $E(v,τ)\not\subseteq F(\mathcal{M},τ)$, then every order-measure continuous and disjointness-preserving mapping $T:E(\mathcal{M},τ)\xrightarrow{\rm into} F(\mathcal{M},τ)$ is identical to the zero mapping, which establishes a noncommutative version of Abramovich's theorem. We also show that every positive isometry $T$ from a normed $\mathcal{M}$-bimodule $E(\mathcal{M},τ)$ of $τ$-measurable operators into another $F(\mathcal{M},τ)$ preserves disjointness provided that the norm of $F(\mathcal{M},τ)$ is strictly monotone. As an application, we obtain the general form of $T$, which extends and unifies several results due to Abramovich, de Jager, Conradie, Veksler and Sukochev et al. \cite{SV,HSZ20,Abra1991,vek,dC20}.

math.FA↗
arXiv2026

A logarithmically monotone symmetric norm which is not fully symmetric

We construct an explicit symmetric Banach norm on a function space over $(0,\infty)$ which is monotone with respect to logarithmic submajorization but is not strongly symmetric, and hence is not fully symmetric. This answers a question raised by Dodds, Dodds, Sukochev, and Zanin. We also construct a strongly symmetric Banach function space over $(0,\infty)$ which is monotone with respect to logarithmic submajorization and admits no equivalent fully symmetric norm.

math.FA↗
arXiv2026

Arazy-type decomposition theorem for bounded linear operators and commutators on the trace class

The classical Arazy's decomposition theorem provides a powerful tool in the study of sequences in (and isomorphisms on) a separable operator ideal $\mathcal C_E$ of the algebra $\mathcal B(H)$ of all bounded linear operators on the separable infinite-dimensional Hilbert space $H$. In this paper, we extend and strengthen Arazy's decomposition theorem to the setting of general bounded linear operators on a separable (quasi-Banach) operator ideal $\mathcal C_E$ of $\mathcal B(H)$. Several applications are given to the study of $\mathcal C_E$-strictly singular operators, largest proper ideals in the algebra $\mathcal B(\mathcal C_E)$ of all bounded linear operators on $\mathcal C_E$ and complementably homogeneous Banach spaces among others. Our versions of decomposition theorems supply tools for a noncommutative generalization of deep commutator theorems for operators on $\ell_p$ and $L_p$, $1\le p <\infty $, due to Brown and Pearcy, Apostol, and Dosev, Johnson and Schechtman. We are able to characterize commutators on the Schatten-von Neumann class $\mathcal C_p$, $1\le p<\infty $. For the crucial case, $p=1$, we establish that any operator $T\in\mathcal B(\mathcal C_1)$ is a commutator if and only if $T$ is not of the form $λI+K$ for some $λ\neq 0$ and $\mathcal C_1$-strictly singular operator $K$.

math.FA↗
arXiv2025

Isometric Structure in Noncommutative Symmetric Spaces

This is a systematic study of isometries between noncommutative symmetric spaces. Let $\mathcal{M}$ be a semifinite von Neumann algebra (or an atomic von Neumann algebra with all atoms having the same trace) acting on a separable Hilbert space $\mathcal{H}$ equipped with a semifinite faithful normal trace $τ$. We show that for any noncommutative symmetric space corresponding to a symmetric function space $E(0,\infty)$ in the sense of Lindenstrauss--Tzafriri such that $\left\|\cdot\right\|_E\ne λ\left\|\cdot\right\|_{L_2}$, $λ\in \mathbb{R}_+$, any isometry on $E(\mathcal{M},τ)$ is of elementary form. This answers a long-standing open question raised in the 1980s in the non-separable setting [Math. Z. 1989], while the case of separable symmetric function spaces was treated in [Huang \& Sukochev, JEMS, 2024]. As an application, we obtain a noncommutative Kalton--Randrianantoanina--Zaidenberg Theorem, providing a characterization of noncommutative $L_p$-spaces over finite von Neumann algebras and a necessary and sufficient condition for an operator on a noncommutative symmetric space to be an isometry. Having this at hand, we answer a question posed by Mityagin in 1970 [Uspehi Mat. Nauk] and its noncommutative counterpart by showing the any symmetric space $E(\mathcal{M},τ)\ne L_p(\mathcal{M},τ)$ over a noncommutative probability is not isometric to a symmetric space over a von Neumann algebra equipped with a semifinite infinite faithful normal trace. It is also shown that any noncommutative $L_p$-space, $1\le p<\infty$, affiliated with an atomless semifinite von Neumann algebra has a unique symmetric structure up to isometries. This contributes to the resolution of an isometric version of Pełczyński's problem concerning the uniqueness of the symmetric structure in noncommutative symmetric spaces.

math.OA↗
arXiv2025

SimPath: Mitigating Motion Sickness in In-vehicle Infotainment Systems via Driving Condition Adaptation

The problem of Motion Sickness (MS) among passengers significantly impacts the comfort and efficiency of In-Vehicle Infotainment Systems (IVIS) use. In this study, we innovatively designed SimPath, a visual design to effectively mitigate passengers' MS and boost their efficiency of using IVIS during driving. The study focuses on the problem of irregular motion conditions frequently encountered during actual driving. To validate the efficacy of this approach, two sets of real - vehicle experiments were carried out in real driving scenarios. The results demonstrate that this approach significantly reduces passenger's MS level to a certain extent. However, due to divided attention from visual content, it does not directly improve the IVIS efficiency. In conclusion, this study offers crucial insights for the design of a more intelligent and user friendly IVIS, based on the discussion of the principle, providing strong theoretical support and practical guidance for the development of future IVIS in autonomous vehicles.

cs.HC↗
arXiv2025

MSAM: Multi-Semantic Adaptive Mining for Cross-Modal Drone Video-Text Retrieval

With the advancement of drone technology, the volume of video data increases rapidly, creating an urgent need for efficient semantic retrieval. We are the first to systematically propose and study the drone video-text retrieval (DVTR) task. Drone videos feature overhead perspectives, strong structural homogeneity, and diverse semantic expressions of target combinations, which challenge existing cross-modal methods designed for ground-level views in effectively modeling their characteristics. Therefore, dedicated retrieval mechanisms tailored for drone scenarios are necessary. To address this issue, we propose a novel approach called Multi-Semantic Adaptive Mining (MSAM). MSAM introduces a multi-semantic adaptive learning mechanism, which incorporates dynamic changes between frames and extracts rich semantic information from specific scene regions, thereby enhancing the deep understanding and reasoning of drone video content. This method relies on fine-grained interactions between words and drone video frames, integrating an adaptive semantic construction module, a distribution-driven semantic learning term and a diversity semantic term to deepen the interaction between text and drone video modalities and improve the robustness of feature representation. To reduce the interference of complex backgrounds in drone videos, we introduce a cross-modal interactive feature fusion pooling mechanism that focuses on feature extraction and matching in target regions, minimizing noise effects. Extensive experiments on two self-constructed drone video-text datasets show that MSAM outperforms other existing methods in the drone video-text retrieval task. The source code and dataset will be made publicly available.

cs.CV↗
arXiv2025

Rank metric isometries and determinant-preserving mappings on II$_1$-factors

We fully describe the general form of a linear (or conjugate-linear) rank metric isometry on the Murray--von Neumann algebra associated with a II$_1$-factor. As an application, we establish Frobenius' theorem in the setting of II$_1$-factors, by showing that every determinant-preserving linear bijection between two II$_1$-factors is necessarily an isomorphism or an anti-isomorphism. This confirms the Harris--Kadison conjecture (1996).

math.OA↗
arXiv2024

Learning Global Object-Centric Representations via Disentangled Slot Attention

Humans can discern scene-independent features of objects across various environments, allowing them to swiftly identify objects amidst changing factors such as lighting, perspective, size, and position and imagine the complete images of the same object in diverse settings. Existing object-centric learning methods only extract scene-dependent object-centric representations, lacking the ability to identify the same object across scenes as humans. Moreover, some existing methods discard the individual object generation capabilities to handle complex scenes. This paper introduces a novel object-centric learning method to empower AI systems with human-like capabilities to identify objects across scenes and generate diverse scenes containing specific objects by learning a set of global object-centric representations. To learn the global object-centric representations that encapsulate globally invariant attributes of objects (i.e., the complete appearance and shape), this paper designs a Disentangled Slot Attention module to convert the scene features into scene-dependent attributes (such as scale, position and orientation) and scene-independent representations (i.e., appearance and shape). Experimental results substantiate the efficacy of the proposed method, demonstrating remarkable proficiency in global object-centric representation learning, object identification, scene generation with specific objects and scene decomposition.

cs.CV↗
arXiv2023

OCTScenes: A Versatile Real-World Dataset of Tabletop Scenes for Object-Centric Learning

Humans possess the cognitive ability to comprehend scenes in a compositional manner. To empower AI systems with similar capabilities, object-centric learning aims to acquire representations of individual objects from visual scenes without any supervision. Although recent advances in object-centric learning have made remarkable progress on complex synthesis datasets, there is a huge challenge for application to complex real-world scenes. One of the essential reasons is the scarcity of real-world datasets specifically tailored to object-centric learning. To address this problem, we propose a versatile real-world dataset of tabletop scenes for object-centric learning called OCTScenes, which is meticulously designed to serve as a benchmark for comparing, evaluating, and analyzing object-centric learning methods. OCTScenes contains 5000 tabletop scenes with a total of 15 objects. Each scene is captured in 60 frames covering a 360-degree perspective. Consequently, OCTScenes is a versatile benchmark dataset that can simultaneously satisfy the evaluation of object-centric learning methods based on single-image, video, and multi-view. Extensive experiments of representative object-centric learning methods are conducted on OCTScenes. The results demonstrate the shortcomings of state-of-the-art methods for learning meaningful representations from real-world data, despite their impressive performance on complex synthesis datasets. Furthermore, OCTScenes can serve as a catalyst for the advancement of existing methods, inspiring them to adapt to real-world scenes. Dataset and code are available at https://huggingface.co/datasets/Yinxuan/OCTScenes.

cs.CV↗
arXiv2023

Innerness of derivations into noncommutative symmetric spaces is determined commutatively

Let $E=E(0,\infty)$ be a symmetric function space and $E(\mathcal{M},τ)$ be a symmetric operator space associated with a semifinite von Neumann algebra with a faithful normal semifinite trace. Our main result identifies the class of spaces $E$ for which every derivation $δ:\mathcal{A}\to E(\mathcal{M},τ)$ is necessarily inner for each $C^*$-subalgebra $\mathcal{A}$ in the class of all semifinite von Neumann algebras $\mathcal{M}$ as those with the Levi property.

math.OA↗
arXiv2023

Hermitian operators and isometries on symmetric operator spaces

Let $\mathcal{M}$ be an atomless semifinite von Neumann algebra (or an atomic von Neumann algebra with all atoms having the same trace) acting on a (not necessarily separable) Hilbert space $H$ equipped with a semifinite faithful normal trace $τ$. Let $E(\mathcal{M},τ) $ be a symmetric operator space affiliated with $ \mathcal{M} $, whose norm is order continuous and is not proportional to the Hilbertian norm $\left\|\cdot\right\|_2$ on $L_2(\mathcal{M},τ)$. We obtain general description of all bounded hermitian operators on $E(\mathcal{M},τ)$. This is the first time that the description of hermitian operators on asymmetric operator space (even for a noncommutative $L_p$-space) is obtained in the setting of general (non-hyperfinite) von Neumann algebras. As an application, we resolve a long-standing open problem concerning the description of isometries raised in the 1980s, which generalizes and unifies numerous earlier results.

math.OA↗
arXiv2022

Isomorphic classification of $L_{p,q}$-spaces, II

This is a continuation of the papers [Kuryakov-Sukochev, JFA, 2015] and [Sadovskaya-Sukochev, PAMS, 2018], in which the isomorphic classification of $L_{p,q}$, for $1< p<\infty$, $1\le q<\infty$, $p\ne q $, on resonant measure spaces, has been obtained. The aim of this paper is to give a complete isomorphic classification of $L_{p,q}$-spaces on general $σ$-finite measure spaces. Towards this end, several new subspaces of $L_{p,q}(0,1)$ and $L_{p,q}(0,\infty)$ are identified and studied.

math.FA↗
arXiv2022

Operator $θ$-Hölder functions with respect to $\left\|\cdot\right\|_p$, $0< p\le \infty$

Let $θ\in(0,1)$ and $(\mathcal{M},τ)$ be a semifinite von Neumann algebra. We consider the function spaces introduced by Sobolev (denoted by $S_{d,θ}$), showing that there exists a constant $d>0 $ depending on $p$, $0 1$, we obtain a reverse of the Birman-Koplienko-Solomjak inequality, which extends a couple of existing results on fractional powers $t\mapsto t^θ$ by Ando et al.

math.FA↗
arXiv2022

Optimal range of Haar martingale transforms and its applications

Let $(\mathcal{F}_n)_{n\ge 0}$ be the standard dyadic filtration on $[0,1]$. Let $\mathbb{E}_{\mathcal{F}_n}$ be the conditional expectation from $ L_1=L_1[0,1]$ onto $\mathcal{F} _n$, $n\ge 0$, and let $\mathbb{E}_{\mathcal{F} _{-1}} =0$. We present the sharp estimate for the distribution function of the martingale transform $T$ defined by \begin{align*} Tf=\sum_{m=0}^\infty \left( \mathbb{E}_{\mathcal{F}_{2m}} f-\mathbb{E}_{\mathcal{F}_{2m-1}}f \right), ~f\in L_1, \end{align*} in terms of the classical Calderón operator. As an application, for a given symmetric function space $E$ on $[0,1]$, we identify the symmetric space $\mathcal{S}_E$, the optimal Banach symmetric range of martingale transforms/Haar basis projections acting on $E$.

math.PR↗
arXiv2020

Lack of isomorphic embeddings of symmetric function spaces into operator ideals

Let $E(0,1)$ be a symmetric space on $(0,1)$ and $C_F$ be a symmetric ideal of compact operators on the Hilbert space $\ell_2$ associated with a symmetric sequence space $F$. We give several criteria for $E(0,1)$ and $ F$ so that $E(0,1)$ does not embed into the ideal $C_F$, extending the result for the case when $E(0,1)=L_p(0,1)$ and $F=\ell_p $, $1\le p<\infty$, due to Arazy and Lindenstrauss.

math.FA↗