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.
Citation
Longfa Sun. Yanpeng Ma. "Stability of $\varepsilon$-isometries on the positive cones of finite-dimensional Banach spaces." Bull. Belg. Math. Soc. Simon Stevin 27 (5) 789 - 800, december 2020. https://doi.org/10.36045/j.bbms.200413
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