【摘 要】
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The study of properties of isometries and its generalizations on Banach spaces has continued for over 80 years since Mazur and Ulams celebrated theorem in 1
【机 构】
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XiamenUniversity,China
【出 处】
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算子代数和调和分析2017年研讨会 (Workshop on Operator Algebras and Harmoni
论文部分内容阅读
The study of properties of isometries and its generalizations on Banach spaces has continued for over 80 years since Mazur and Ulams celebrated theorem in 1932: Every surjective isometry from a Banach space X to a Banach space Y is necessarily affine.A mapping f∶X → Y is said to be ε-isometry(for some ε≥ 0)provided |‖f(x)-f(y)‖-‖x-y‖|≤ε,(A)x,y∈X.We say that an "-isometry f is standard,if f(0)= 0; and a 0-isometry is called an isometry.In this talk,we first give a sequence of examples showing linear isometries,isometries and perturbed isometries have extensive backgrounds in both pure mathematics and applied mathematics.Then we present a brief survey on this topic.Finally,we conclude this talk by some open questions in this research area.
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