Stability of a Pair of Banach Spaces for ε-Isometries
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A pair of Banach spaces (X, Y) is said to be stable if for every ε-isometry f : X → Y, there exist γ > 0 and a bounded linear operator T : L(f ) → X with ‖T‖ ≤ α such that ‖Tf (x) — x‖ ≤ γε for all x ∈ X, where L(f ) is the closed linear span of f (X). In this article, we study the stability of a pair of Banach spaces (X, Y) when X is a C(K) space. This gives a new positive answer to Qian’s problem. Finally, we also obtain a nonlinear version for Qian’s problem.
Key wordsStability ε-isometry Figiel theorem Banach space
2010 MR Subject Classification46B04 46B20 54C60
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- Holmes R B. Geometric Functional Analysis and its Applications. Graduate Texts in Mathematics. Vol 24. New York: Springer, 1975Google Scholar
- Phelps R R. Convex functions, monotone operators and differentiability. Lecture Notes in Mathematics 1364. Springer, 1989Google Scholar