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On Halmos'third problem on Banach spaces: 《Science China Mathematics》2025年第2期399-420,共22页Lixin Cheng Junsheng Fang Chunlan Jiang; supported by National Natural Science Foundation of China(Grant Nos.12271453,12071109,11471271,11471270)。; In 1970,Halmos posed ten open problems in Hilbert spaces.The third problem asks:If an intransitive operator T has an inverse,is its inverse also intransitive?This question is closely related to the invariant subspace ...; 关键词：invariant subspace bounded linear operator Banach space

Splitting Method for Support Vector Machine in Reproducing Kernel Banach Space with a Lower Semi-continuous Loss Function: 《Chinese Annals of Mathematics,Series B》2024年第6期823-854,共32页Mingyu MO Yimin WEI Qi YE; supported by the National Natural Science Foundation of China(Nos.12026602,12071157,12271108);the Natural Science Foundation of Guangdong Provience(No.2024A1515012288);the Science and Technology Commission of Shanghai Municipality(No.23JC1400501);the Ministry of Science and Technology of China(No.G2023132005L).; In this paper,the authors employ the splitting method to address support vector machine within a reproducing kernel Banach space framework,where a lower semi-continuous loss function is utilized.They translate support...; 关键词：Support vector machine Lower semi-continuous loss function Repro-ducing kernel Banach space Tensor optimization problem Splitting method

Some Mean Convergence Theorems for the Maximum of Normed Double Sums of Banach Space Valued Random Elements: 《Acta Mathematica Sinica,English Series》2024年第7期1727-1740,共14页Andrew ROSALSKY Le Van THANH Nguyen Thi THUY; In this correspondence,we establish mean convergence theorems for the maximum of normed double sums of Banach space valued random elements.Most of the results pertain to random elements which are M-dependent.We expand...; 关键词：Double sum mean convergence Rademacher type p Banach space Banach space valued random element M-dependent random elements

ON A UNIVERSAL INEQUALITY FOR APPROXIMATE PHASE ISOMETRIES: 《Acta Mathematica Scientia》2024年第3期823-838,共16页戴端旭阙海新孙龙发郑本拓; supported by the NSFC(12126329,12171266,12126346);the NSF of Fujian Province of China(2023J01805);the Research Start-Up Fund of Jimei University(ZQ2021017);supported by the NSFC(12101234);the NSF of Hebei Province(A2022502010);the Fundamental Research Funds for the Central Universities(2023MS164);the China Scholarship Council;supported by the Simons Foundation(585081)。; Let X and Y be two normed spaces.Let U be a non-principal ultrafilter on N.Let g:X→Y be a standard ε-phase isometry for someε≥ 0,i.e.,g(0)=0,and for all u.v ∈ X,||‖g(u)+g(v)‖±‖g(u)-g(v)‖|-|‖u+v‖±‖u-v‖| ...; 关键词：ε-phase isometry phase isometry Banach space

STABILITY AND CONVERGENCE OF STEPSIZE-DEPENDENT LINEAR MULTISTEP METHODS FOR NONLINEAR DISSIPATIVE EVOLUTION EQUATIONS IN BANACH SPACE: 《Journal of Computational Mathematics》2024年第2期337-354,共18页Wansheng Wang; supported by the Natural Science Foundation of China(Grant Nos.12271367,11771060);by the Science and Technology Innovation Plan of Shanghai,China(Grant No.20JC1414200);sponsored by the Natural Science Foundation of Shanghai,China(Grant No.20ZR1441200).; Stability and global error bounds are studied for a class of stepsize-dependent linear multistep methods for nonlinear evolution equations governed by ω-dissipative vector fields in Banach space.To break through the ...; 关键词：Nonlinear evolution equation Linear multistep methods ω-dissipative operators Stability CONVERGENCE Banach space

Weakly Compact Sets and Riesz Representation Theorem in Musielak Sequence Spaces: 《Acta Mathematica Sinica,English Series》2024年第2期467-484,共18页Wan Zhong GONG Si Yu SHI Zhong Rui SHI; Supported by the National Natural Science Foundation of China(Grant No.11771273)。; In this work,we give some criteria of the weakly compact sets and a representation theorem of Riesz's type in Musielak sequence spaces using the ideas and techniques of sequence spaces and Musielak function.Finally,as...; 关键词：Compact set weak topology Banach space dual space Musielak sequence spaces

Variational Analysis Based on Proximal Subdifferential on Smooth Banach Spaces: 《Acta Mathematica Sinica,English Series》2024年第2期595-618,共24页Xi Yin ZHENG; Supported by the National Natural Science Foundation of P.R.China(Grant No.12171419)。; 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 deve...; 关键词：Smooth Banach space proximal subdifferential proximal normal cone KKT condition

Feynman Path Integral Using Operator Integration in Banach Space: 《Journal of Applied Mathematics and Physics》2024年第2期432-444,共13页Reza R. Ahangar Erbil Cetin Serife Muge Ege; Feynman-Path Integral in Banach Space: In 1940, R.P. Feynman attempted to find a mathematical representation to express quantum dynamics of the general form for a double-slit experiment. His intuition on several slits...; 关键词：Feynman Path Integral Lebesgue-Bochner-Stieltjes Integral Operator Integral Particle-Wave Function Operator Integration Position and Momentum Operators

Generalization of Inequalities in Metric Spaces with Applications: 《Journal of Applied Mathematics and Physics》2023年第10期2923-2931,共9页Eltigani I. Hassan; In this paper, which serves as a continuation of earlier work, we generalize the idea of inequalities in metric spaces and use them to demonstrate that the incomplete metric space can be used to obtain a Banach space.; 关键词：Metric Spaces Banach Space INEQUALITIES

A Universal Inequality for Stability of Coarse Lipschitz Embeddings: 《Acta Mathematica Sinica,English Series》2023年第9期1805-1816,共12页Duan Xu Dai Ji Chao Zhang Quan Qing Fang Long Fa Sun Ben Tuo Zheng; Supported by National Natural Science Foundation of China(Grant Nos.12126329,12171266,12126346,12101234);Simons Foundation(Grant No.585081);Educational Commission of Fujian Province(Grant No.JAT190589);Natural Science Foundation of Fujian Province(Grant No.2021J05237);the research start-up fund of Jimei University(Grant No.ZQ2021017);the research start-up fund of Putian University(Grant No.2020002);the Natural Science Foundation of Hebei Province(Grant No.A2022502010);the Fundamental Research Funds for the Central Universities(Grant No.2023MS164);the Natural Science Foundation of Fujian Province(Grant No.2023J01805)。; Let X and Y be two pointed metric spaces.In this article,we give a generalization of the Cheng-Dong-Zhang theorem for coarse Lipschitz embeddings as follows:If f:X→Y is a standard coarse Lipschitz embedding,then for ...; 关键词：Lindenstrauss Problem coarse Lipschitz embedding coarse stability Banach space

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