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Nuclearity and Finite-Representability in the System of Completely Integral Mapping Spaces

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Acta Mathematica Sinica,English Series 2024年第5期40卷 1197-1214页

作者： Zhe DONg Ji Cheng TAO Ya Fei ZHAO department of mathematics Zhejiang UniversityHangzhou 310027P.R.China department of mathematics China Jiliang UniversityHangzhou 310018P.R.China department of mathematics Zhejiang International Studies UniversityHangzhou 310023P.R.China

In this paper,we investigate local properties in the system of completely integral mapping *** introduce notions of injectivity,local reflexivity,exactness,nuclearity,finite-represent ability and WEp in the system of completely integral mapping *** we obtain that any finite-dimensional operator space is injective in the system of completely integral mapping *** we prove that C is the unique nuclear operator space and the unique exact operator space in this *** also show that C is the unique operator space which is finitely representable in{T_(n)}n∈Nin this *** corollaries,Kirchberg’s conjecture and QWEp conjecture in the system of completely integral mapping spaces are false.

关键词： Completely integral mapping space injectivity exactness nuclearity finite-representability WEp

Toeplitz Operators and Carleson Measures for Weighted Bergman Spaces Induced by Regular Weights

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Acta Mathematica Sinica,English Series 2024年第5期40卷 1345-1359页

作者： Jun Tao DU Song Xiao Hasi WULAN department of mathematics Guangdong University of Petrochemical TechnologyMaoming 525000P.R.China department of mathematics Shantou UniversityShantou 515063P.R.China

In this paper,we give a universal description of the boundedness and compactness of Toeplitz operator T_(μ)^(ω)between Bergman spaces A_(η)^(p)and A_(υ)^(q)whenμis a positive Borel measure,1p,qgular *** using Khinchin’s inequality and Kahane’s inequality,we get a new characterization of the Carleson measure for Bergman spaces induced by regular weights.

关键词： Bergman space Carleson measure Toeplitz operator regular weight

Variational Analysis Based on proximal Subdifferential on Smooth Banach Spaces

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Acta Mathematica Sinica,English Series 2024年第2期40卷 595-618页

作者： Xi Yin ZHENg department of mathematics Yunnan UniversityKunming 650091P.R.China

This paper first shows that for any p∈(1,2)there exists a continuously differentiable function f on l^(p)(and L^(p))such that the proximal subdifferential of f is empty everywhere,and hence it is not suitable to develop theory on proximal subdifferential in the classical Banach spaces l^(p)and L^(p) with p∈(1,2).On the other hand,this paper establishes variational analysis based on the proximal subdifferential in the framework of smooth Banach spaces of power type 2,which conclude all Hilbert spaces and all the classical spaces l^(p)and L^(p)with p∈(2,+∞).In particular,in such a smooth space,we provide the proximal subdifferential rules for sum functions,product functions,composite functions and supremum functions,which extend the basic results on the proximal subdifferential established in the framework of Hilbert *** of our main results are new even in the Hilbert space *** applications,we provide KKT-like conditions for nonsmooth optimization problems in terms of proximal subdifferential.

关键词： Smooth Banach space proximal subdifferential proximal normal cone KKT condition

Relative Broken Family Sensitivity

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Acta Mathematica Sinica,English Series 2024年第9期40卷 2297-2306页

作者： Zhuo Wei LIU Tao YU department of mathematics Shantou UniversityShantou 515063P.R.China

Letπ:(X,T)→(Y,S)be a factor map between two topological dynamical systems,and F_(a) Furstenberg family of *** introduce the notion of relative broken *** Fs(***,Finf)be the families consisting of all syndetic subsets(*** upper Banach density subsets,infinite subsets).We show that for a factor mapπ:(X,T)→(Y,S)between transitive systems,πis relatively broken F-sensitive for F=Fs or Fpubd if and only if there exists a relative sensitive pair which is an F-recurrent point of(R_(π),T^((2)));is relatively broken Finf-sensitive if and only if there exists a relative sensitive pair which is not *** a factor mapπ:(X,T)→(Y,S)between minimal systems,we get the structure of relative broken F-sensitivity by the factor map to its maximal equicontinuous factor.

关键词： Relative sensitivity recurrent points Furstenberg family relative sensitive pairs maximal equicontinuous factor

Hall Algebras and Quantum Symmetric pairs of Kac-Moody Type Ⅱ

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Acta Mathematica Sinica,English Series 2024年第3期40卷 806-822页

作者： Ming LU Run Ze SHANg department of mathematics Sichuan UniversityChengdu 610064P.R.China

We extend the ■Hall algebra realization of ■quantum groups arising from quantum symmetric pairs,which establishes an injective homomorphism from the universal ■quantum group of Kac-Moody type to the ■Hall algebra ... 详细信息

关键词： Quantum symmetric pairs Hall algebras Quiver with involutions

global Spherically Symmetric Solutions for a Coupled Compressible Navier–Stokes/Allen–Cahn System

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Acta Mathematica Sinica,English Series 2024年第8期40卷 2037-2064页

作者： Chang Ming SONg Jian Lin ZHANg Yuan Yuan WANg department of Applied mathematics School of Mathematics and Information ScienceZhongyuan University of TechnologyZhengzhou 450007P.R.China

In this paper,we consider the global spherically symmetric solutions for the initial boundary value problem of a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of two-phase viscous compressible *** prove the existence and uniqueness of global classical solution,weak solution and strong solution under the assumption of spherically symmetry condition for initial dataρ0 without vacuum state.

关键词： Diffuse interface model global solutions Navier-Stokes equations Allen-Cahn equation spherically symmetry

Finite groups with Some Bounded Codegrees

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1778-1784页

作者： Dong Fang YANg Yu ZENg Heng LV School of mathematics and Statistics Southwest UniversityChongqing400715P.R.China department of mathematics Changshu Institute of TechnologyChangshu215500P.R.China

For a characterχof a finite group g,the number cod(χ) := ∣g:ker(χ)∣/χ(1)is called the codegree ofχ.In this paper,we give a solvability criterion for a finite group g depending on the minimum of the ratioχ(1)^(... 详细信息

关键词： Finite group codegree degree simple group

Some Rotundities of Orlicz–Lorentz Spaces

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Acta Mathematica Sinica,English Series 2024年第8期40卷 1893-1919页

作者： Wan Zhong gONg peng WANg department of mathematics Anhui Normal UniversityWuhu 241000P.R.China

K-UR,K-LUR and K-R are the generalizations of UR,LUR and R respectively,which are of great significance in Banach space *** in Orlicz–Lorentz function spaceΛ_(ϕ,ω)^(◦)[0,γ)equipped with the Orlicz norm,the research methods of K-UR,K-LUR and K-R are much more complicated than those of UR,LUR and *** this paper we obtain some criteria of K-UR,K-LUR and K-R ofΛ_(ϕ,ω)^(◦)[0,γ)by means of the norm of dual space and H_(μ)property ofΛ_(ϕ,ω)^(◦)[0,γ).

关键词： Orlicz-Lorentz space Orlicz norm k-uniform rotundity locally k-uniform rotundity krotundity

Spacelike Framed Curves with Lightlike Components and Singularities of Their Evolutes and Focal Surfaces in Minkowski 3-space

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1521-1532页

作者： peng Cheng LI Dong He pEI Xin ZHAO School of mathematics and Statistics Northeast Normal UniversityChangchun 130024P.R.China department of mathematics Harbin Institute of TechnologyWeihai 264209P.R.China School of mathematics and Statistics Qingdao UniversityQingdao 266071P.R.China

In this paper,we define the evolute and focal surface of a spacelike framed curve with lightlike components in Minkowski *** is a generalization of the previous results of regular spacelike curves,since singularities are allowed in the original spacelike curves studied by spacelike framed curves with lightlike ***,we show a new geometric invariant to characterise singularities of the focal ***,the classification theorem and recognition theorem for the singularities of the focal surface in generic are also given.

关键词： Evolutes focal surfaces spacelike framed curves singularities