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.
Duanxu DAI
,
Bentuo ZHENG
. STABILITY OF A PAIR OF BANACH SPACES FOR ε-ISOMETRIES[J]. Acta mathematica scientia, Series B, 2019
, 39(4)
: 1163
-1172
.
DOI: 10.1007/s10473-019-0418-9
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