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- W3197591711 abstract "Let $ mathcal{X}$, $ mathcal{Y}$ be Banach spaces and $S:mathcal{X} to mathcal{Y} $ be an invertible Lipschitz map. Let $ T : mathcal{X}rightarrow mathcal{Y}$ be a map and there exist $ lambda_1,lambda_2 in left [0, 1 right )$ such that begin{align*} |Tx-Ty-(Sx-Sy)|leqlambda_1|Sx-Sy|+lambda_2|Tx-Ty|,quad forall x,y in mathcal{X}. end{align*} Then we prove that $T$ is an invertible Lipschitz map. This improves 25 years old Casazza-Kalton-Christensen-van Eijndhoven perturbation. It also improves 28 years old Soderlind-Campanato perturbation and 2 years old Barbagallo-Ernst-Thera perturbation. We give applications to the theory of metric frames. The notion of Lipschitz atomic decomposition for Banach spaces is also introduced." @default.
- W3197591711 created "2021-09-13" @default.
- W3197591711 creator A5017350612 @default.
- W3197591711 date "2021-09-05" @default.
- W3197591711 modified "2023-09-27" @default.
- W3197591711 title "Improving Casazza-Kalton-Christensen-van Eijndhoven Perturbation with Applications" @default.
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