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A note on the stability of nonsurjective ε-isometries of Banach spaces.
- Source :
-
Proceedings of the American Mathematical Society . Nov2020, Vol. 148 Issue 11, p4837-4844. 8p. - Publication Year :
- 2020
-
Abstract
- Let X, Y be Banach spaces, and let ƒ : X → Y be an ε-isometry with ƒ(0) = 0 for some ε ≥ 0. In this paper, we show that for every x* ∈ X*, there exists φ ∈ Y* with ||φ|| = ||x*|| ≡ r such that |<x*,x>| − <φ,ƒ(x)>| ≤ 3rε, ∨x ∈ X. Moreover, the constant ''3'' is the best one in general. [ABSTRACT FROM AUTHOR]
- Subjects :
- *BANACH spaces
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 148
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 145454155
- Full Text :
- https://doi.org/10.1090/proc/15110