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The representation theorem of onto isometric mappings between two unit spheres of l∞-type spaces and the application on isometric extension problem

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Science China Mathematics 2004年第5期47卷 722-729页

作者： ding guanggui School of Mathematical Sciences and LPMC Nankai University Tianjin 300071 China

In this paper, we first derive the representation theorem of onto isometric mappings in the unit spheres of real l∞-type spaces, then we conclude that such mappings can be extended to the whole space as (real) linear... 详细信息

关键词： isometric mapping, isometric extension.

Small into Isomorphisms on L_∞ Spaces

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Acta Mathematica Sinica,English Series 1995年第4期11卷 417-421页

作者： guanggui ding Department of Mathematics Nankai University Tianjin China

If T is an isomorphism of L∞（A,μ）into L∞（B,v）which satisfies the condition ||T|| ||T-1||≤1+ε,where（A,μ）is a σ-finite measure space then T/||T||is close to an isometry with an error less than 4ε1.

关键词： Periodic orbits Competitive(cooperative)systems Invariant surface

On isometric extension problem between two unit spheres

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Science China Mathematics 2009年第10期52卷 2069-2083页

作者： ding guanggui School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China School of Mathematical Sciences and LPMC Nankai University Tianjin China

In this paper we introduce the isometric extension problem of isometric mappings between two unit spheres. Some important results of the related problems are outlined and the recent progress is mentioned.

关键词： normed space isometric extension isometric mapping 1-Lipschitz mapping 46A22 46B02 46B04 46B20 46B22

The isometric extension of “into” mappings on unit spheres of AL-spaces

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Science China Mathematics 2008年第10期51卷 1904-1918页

作者： ding guanggui School of Mathematics Science, Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China School of Mathematics Science Chern Institute of Mathematics and LPMC Nankai University Tianjin China

In this paper, we show that if V0 is an isometric mapping from the unit sphere of an AL-space onto the unit sphere of a Banach space E, then V0 can be extended to a linear isometry defined on the whole space.

关键词： isometric extension (atomic) AL-space

THE UNIFORM BOUNDEDNESS PRINCIPLE IN SOME TOPOLOGICAL VECTOR GROUPS

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Systems Science and Mathematical Sciences 2000年第3期13卷 292-301页

作者： ding guanggui(Department of Mathematics, Nankai University, Tianjin 300071, China) 南开大学数学系天津 300071

It is shown that the famous Banach-Steinhaus theorem can be generalized to some families of nonlinear functionals defined on some topological groups and topological vector space, e.g. the F-spaced lβ(0 <β < 1) and S... 详细信息

关键词： Binary fissionable topological group locally pseudo-bounded second category uniform boundedness principle

A NOTE ON THE EQUICONTINUITY IN SOME TOPOLOGICAL GROUPS

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Systems Science and Mathematical Sciences 1999年第3期12卷 270-272页

作者： ding guanggui(Department of Mathematics, Nankai University, Tianjin 300071, China) 南开大学数学系天津 300071

In this paper, we show that a theorem concerning the equicontinuity of theoperators in F-spaces can be generalized to a class of operators defined on the binaryfissionable topological groups.

关键词： Binary fissionable topological group quasi-additive operator equicontinuity.