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On Principal Invariant Subspaces

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Acta Mathematica Sinica,English Series 2015年第10期31卷 1621-1628页

作者： xiao Ming XU xiao chun fang School of Science Shanghai Institute of Technology Department of Mathematics Tongji University

Let F and G be closed subspaces of the complex Hilbert spaceH, and U and V be closed subspaces of F- and G, respectively. In this paper, using the technique of operator block, we present the necessary and sufficient conditions under which （U, V） is a pair of （strictly, non-degenerate） principal invariant subspaces for （F, G）.

关键词： Hilbert space operator matrix invariant subspace principal invariant subspace

Common Properties of the Operator Products in Local Spectral Theory

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Acta Mathematica Sinica,English Series 2015年第11期31卷 1715-1724页

作者： Kai YAN xiao chun fang Department of Mathematics Tongji University

Let X,Y be Banach spaces, A,D ： X - Y and B,C ： Y - X be the bounded linear operators satisfying operator equation set ACD=DBD DBA=ACAIn this paper, we show that AC and BD share some basic operator properties such as the injectivity and the invertibility. Moreover, we show that AG＇ and BD share many common local spectral properties including SVEP, Bishop property （β） and Dunford property （C）.

关键词： Jacobson's lemma operator equation set common property local spectral theory

Comparison Properties for Asymptotically Tracially Approximation C^(*)-algebras

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Acta Mathematica Sinica,English Series 2023年第5期39卷 863-884页

作者： Qing Zhai FAN xiao chun fang College of Education Shanghai Jian Qiao UniversityShanghai 201306P.R.China Department of Mathematics Shanghai Maritime UniversityShanghai 201306P.R.China Department of Mathematics Tongji UniversityShanghai 200092P.R.China

We show that the following properties of the C*-algebras in a class P are inherited by simple unital C*-algebras in the class of asymptotically tracially in P :(1) n-comparison,(2) α-comparison(1 ≤ α < ∞).

关键词： C*-algebras asymptotically tracially approximation Cuntz semigroup

Lifting Unitary Elements with Application to Approximately Inner Automorphisms

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Acta Mathematica Sinica,English Series 2007年第10期23卷 1745-1750页

作者： xiao chun fang Shu Dong LIU Department of Mathematics Tongji University Shanghai 200092 P. R. China Department of Mathematics Qufu Normal University Qufu 273165 P. R. CHina

Let A be a separable unital nuclear simple C＊-algebra with torsion K0 （A）, free K1 （A） and with the UCT. Let T ： A→M（K）/K be a unital homomorphism. We prove that every unitary element in the commutant of T（A） is an exponent, thus it is liftable. We also prove that each automorphism α on E with α ∈ Aut0（A） is approximately inner, where E is a unital essential extension of A by K and α is the automorphism on A induced by α.

关键词： C*-algebra extension automorphism

Partial Isometries and an Invariant of C＊-algebras

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Acta Mathematica Sinica,English Series 2011年第4期27卷 799-806页

作者： Hong Liang YAO xiao chun fang School of Science Nanjing University of Science and Technology Nanjing 210014 P. R. China Department of Mathematics Tongji University Shanghai 200092 P. R. China

In this paper, we will discuss some properties of biprojection-commutative elements which are relevant to the classification of certain infinite C＊-algebras,, and define an important invariant s（A） of C＊-algebra A as well as give some basic properties with regard to s（A）. Moreover we prove that the invariant s（A） has continuity.

关键词： Partial isometry C*-algebra K1-group

The α-comparison Property and Finite Nuclear Dimension of Generalized Inductive Limits for C~*-algebras

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Acta Mathematica Sinica,English Series 2018年第9期34卷 1417-1428页

作者： Yue Liang LIANG xiao chun fang School of Science North University of China Taiyuan 030051 P. R. China Department of Mathematics Tongji University Shanghai 200092 P. R. China

The paper is devoted to the study of generalized inductive limit of C＊-algebras with coherent maps being completely positive contractions of order zero： the nuclear dimension of generalized inductive limit of C＊-algebras with finite nuclear dimension is finite; the generalized inductive limits of C＊-algebras with the α-comparison property also have the s-comparison property.

关键词： Finite nuclear dimension α-comparison property generalized inductive limit of C*-algebras

A Class of C^(*)-Algebras with Non-stable K_1-Group Property

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Acta Mathematica Sinica,English Series 2012年第5期28卷 983-988页

作者： Qing Zhai FAN xiao chun fang Department of Mathematics Shanghai Maritime University Department of Mathematics Tongji University

In this paper, we give a class of C＊-algebras with non-stable K1-group property which include the example non-simple tracial topological rank zero and stable rank two C＊-algebra given by Lin and Osaka.

关键词： C*-Algebras stable rank non-stable

Γ-inverses of Bounded Linear Operators

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Acta Mathematica Sinica,English Series 2014年第4期30卷 675-680页

作者： xiao Ming XU Hong Ke DU xiao chun fang School of Science Shanghai Institute of Technology College of Mathematics and Information Science Shaanxi Normal University Department of Mathematics Tongji University

Let B（Н） be the algebra of all the bounded linear operators on a Hilbert space Н. For A, P and Q in B（Н）, if there exists an operator X ∈ B（Н） such that APXQA = A, XQAPX = X, （QAPX）^＊ = QAPX and （XQAP）^＊ = XQAP, then X is said to be the F-inverse of A associated with P and Q, and denoted by A^＋P,Q. In this note, we present some necessary and sufficient conditions for which A^＋P,Q exists, and give an explicit representation of A^＋PQ （if A^＋P,Q exists）.

关键词： Generalized inverse F-inverse Moore-Penrose inverse

Clinical Characteristics of H1N1 Influenza A-Associated Mild Encephalopathy with Reversible Splenial Lesion: 4 Pediatric Cases

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Current Medical Science 2021年第4期41卷 815-820页

作者： Xu-fang LI Bin AI Jia-wei YE Li-mei TAN Hua-mei YANG chun-xiao fang Lan-hui SHE Yi XU Department of Infectious Disease Guangzhou Women and Children's Medical CenterGuangzhou 510000China

Objective Mild encephalopathy with reversible splenial lesion(MERS)is associated with a variety of infections and anti-epileptic drug *** we report the clinical characteristics of H1N1 influenza A-associated MERS based on our experience of four pediatric *** A detailed retrospective analysis of four patients with H1N1 influenza A-associated MERS was performed at Guangzhou Women and Children’s Medical *** All patients exhibited mild influenza-like illness and *** patients presented with a new-onset seizure with fever after 5 years of age.75%patients had altered mental *** all four patients,influenza A(H1N1)viral RNA was detected in throat swab specimens at least *** magnetic resonance images revealed similar ovoid lesions in the corpus callosum,mainly in the splenium and for one patient in the splenium and genu of the corpus *** one patient had an abnormal electroencephalogram *** and protein in the cerebrospinal fluid were normal in all *** patients received oseltamivir and one patient received intravenous *** a result,all patients fully recovered after 2 months and showed no neurologic sequelae at *** This case series provides insight towards clinical features of H1N1 influenza A-associated MERS.

关键词： mild encephalopathy with reversible splenial lesion H1N1 influenza A children corpus callosum encephalopathy