STABILITY OF ε-ISOMETRIES ON L∞-SPACES

doi:10.1007/s10473-019-0619-2

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (6): 1733-1742.doi: 10.1007/s10473-019-0619-2

• 论文 • 上一篇

STABILITY OF ε-ISOMETRIES ON L_∞-SPACES

戴端旭

College of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China

收稿日期:2018-03-09 修回日期:2019-05-09 出版日期:2019-12-25 发布日期:2019-12-30
作者简介:Duanxu DAI,E-mail:dduanxu@163.com
基金资助:
This work was supported by the Natural Science Foundation of China (11601264), and the Natural Science Foundation of Fujian Province of China (2019J05103), and the Outstanding Youth Scientific Research Personnel Training Program of Fujian Province and the High level Talents Innovation and Entrepreneurship Project of Quanzhou City (2017Z032).

STABILITY OF ε-ISOMETRIES ON L_∞-SPACES

Duanxu DAI

College of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China

Received:2018-03-09 Revised:2019-05-09 Online:2019-12-25 Published:2019-12-30
Supported by:
This work was supported by the Natural Science Foundation of China (11601264), and the Natural Science Foundation of Fujian Province of China (2019J05103), and the Outstanding Youth Scientific Research Personnel Training Program of Fujian Province and the High level Talents Innovation and Entrepreneurship Project of Quanzhou City (2017Z032).

摘要/Abstract

摘要： In this article, we discuss the stability of ε-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.

关键词: stability, ε-isometry, L_∞-space

Abstract: In this article, we discuss the stability of ε-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.

Key words: stability, ε-isometry, L_∞-space

中图分类号:

46B04

戴端旭. STABILITY OF ε-ISOMETRIES ON L_∞-SPACES[J]. 数学物理学报(英文版), 2019, 39(6): 1733-1742.

Duanxu DAI. STABILITY OF ε-ISOMETRIES ON L_∞-SPACES[J]. Acta mathematica scientia,Series B, 2019, 39(6): 1733-1742.

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STABILITY OF ε-ISOMETRIES ON L_∞-SPACES

STABILITY OF ε-ISOMETRIES ON L_∞-SPACES

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