Stability of $\varepsilon$-isometries on the positive cones of finite-dimensional Banach spaces

Pub Date : 2020-12-01 DOI:10.36045/j.bbms.200413
Longfa Sun, Ya-jing Ma
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Abstract

A weak stability bound for the $\varepsilon$-isometry $f$ form the positive cone of a reflexive, strictly convex and Gateaux smooth Banach lattice $X$ to a Banach space $Y$ is presented. This result is used to prove the stability theorem for the $\varepsilon$-isometry $f:(\mathbb{R}^n)^+\rightarrow Y$, where $\mathbb{R}^n$ is the $n$-dimensional space equipped with a $1$-unconditional norm and $Y$ is a n-dimensional, strictly convex and Gateaux smooth space.
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有限维Banach空间正锥上$\varepsilon$-等距的稳定性
给出了自反的严格凸的Gateaux光滑的Banach格$X$到Banach空间$Y$的正锥的$\varepsilon$ -等距$f$的弱稳定性界。该结果用于证明$\varepsilon$ -等距$f:(\mathbb{R}^n)^+\rightarrow Y$的稳定性定理,其中$\mathbb{R}^n$为具有$1$ -无条件范数的$n$维空间,$Y$为n维严格凸和Gateaux光滑空间。
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