| 摘 要： | LetX,Y be two real Banach spaces andε≥0.A map f:X→Y is said to be a standardε-isometry if|f(x)f(y)x y|≤εfor all x,y∈X and with f(0)=0.We say that a pair of Banach spaces(X,Y)is stable if there existsγ0 such that,for every suchεand every standardε-isometry f:X→Y,there is a bounded linear operator T:L(f)≡spanf(X)→X so that T f(x)x≤γεfor all x∈X.X(Y)is said to be universally left-stable if(X,Y)is always stable for every Y(X).In this paper,we show that if a dual Banach space X is universally left-stable,then it is isometric to a complemented w-closed subspace of∞(Γ)for some setΓ,hence,an injective space;and that a Banach space is universally left-stable if and only if it is a cardinality injective space;and universally left-stability spaces are invariant.
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