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| 1 | Stability Characterizations of ε-isometries on Certain Banach Spaces显示文摘Suppose that X, Y are two real Banach Spaces. We know that for a standard ε-isometry f : X → Y, the weak stability formula holds and by applying the formula we can induce a closed subspace N of *. In this paper, by using again the weak stability formula, we further show a sufficient and necessary condition for a standard ε-isometry to be stable in assuming that N is w*-closed in Y*.Making use of this result, we improve several known results including Figiel’s theorem in reflexive spaces.We also prove that if, in addition, the space Y is quasi-reflexive and hereditarily indecomposable, then L(f)≡span[f(X)] contains a complemented linear isometric copy of X;Moreover, if X =Y, then for every e-isometry f: X → X, there exists a surjective linear isometry S:X → X such that f-S is uniformly bounded by 2ε on X. | Li Xin CHENG Long Fa SUN | 2019 | Acta Mathematica Sinica,English Series2019，35，1： | 2 |
| 2 | STABILITY OF A PAIR OF BANACH SPACES FOR ε-ISOMETRIES显示文摘A pair of Banach spaces (X, Y) is said to be stable if for every ￡-isometry f : X→Y,there exist γ> 0 and a bounded linear operator T : L(f)→X with ||T||≤α such that ||Tf(x)- x||≤γε for all x ∈ X, where L(f) is the closed linear span of f(X). In this article, we study the stability of a pair of Banach spaces (X, Y) when X is a C(K) space. This gives a new positive answer to Qian's problem. Finally, we also obtain a nonlinear version for Qian's problem. | 戴端旭 郑本拓 | 2019 | Acta Mathematica Scientia2019，39，4： | 1 |
| 3 | Banach空间的保度量(等距)映射显示文摘Banach空间的保度量(等距)映射研究自从Mazur-Ulam定理(1932)(Banach空间之间的保度量满射一定是仿射映射)开始,已经进行了80多年.本文主要对Banach空间上的保度量映射、或者等距映射及其推广形式—扰动等距和粗等距的研究历史进行回顾,同时也包含一些新的结果.本文重点放在近十年来的研究进展,以及目前该领域所关注的问题介绍. | 程立新 | 2020 | 中国科学:数学2020，50，12： | 0 |
| 4 | STABILITY OF ε-ISOMETRIES ON L_∞-SPACES显示文摘In this article,we discuss the stability ofε-isometries for L∞,λ-spaces.Indeed,we first study the relationship among separably injectivity,injectivity,cardinality injectivity and universally left stability of L∞,λ-spaces as well as we show that the second duals of universally left-stable spaces are injective,which gives a partial answer to a question of Bao-Cheng-Cheng-Dai,and then we prove a sharpen quantitative and generalized Sobczyk theorem which gives examples of nonseparable L∞-spaces X(but not injective)such that the couple(X,Y)is stable for every separable space Y.This gives a new positive answer to Qian's problem. | 戴端旭 | 2019 | Acta Mathematica Scientia2019，39，6： | 0 |
| 5 | Hilbert空间等价类的万有右稳定性显示文摘研究了Hilbert空间等价类的万有右稳定性,得到如下结果:若Banach空间Y同构于一Hilbert空间,则Y是万有右稳定的当且仅当对于任意的可分Banach空间X,Banach空间对(X,Y)是稳定的. | 卫倩 夏红川 | 2018 | 信阳师范学院学报(自然科学版)2018，31，2： | 0 |
| 6 | 关于泛函分析若干问题的进展显示文摘对泛函分析中的若干问题在近年来的进展作一简要介绍,内容包括Banach空间中的球覆盖性质、Banach空间的保度量(等距)映射、Banach空间中的超弱紧集合、Banach空间的非紧性测度、非线性泛函分析和量子信息与算子理论交叉.主要偏重作者及其合作者在这些方面所做的一点工作. | 程庆进 杜拴平 刘轼波 张文 | 2023 | 厦门大学学报(自然科学版)2023，62，6： | 0 |
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