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Universal stability of Banach spaces for ε -isometries

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Cheng L., Dai D., Dong Y., Zhou Y.

Studia Mathematica

2014

tom 221

nr 2

141-149

Let X, Y be real Banach spaces and ε > 0. A standard ε-isometry f: X → Y is said to be (α,γ)-stable (with respect to $T: L(f) ≡ \overline{span}f(X) → X$ for some α,γ > 0) if T is a linear operator with ||T|| ≤ α such that Tf- Id is uniformly bounded by γε on X. The pair (X,Y) is said to be stable if every standard ε-isometry f: X → Y is (α,γ)-stable for some α,γ > 0. The space X[Y] is said to be universally left [right]-stable if (X,Y) is always stable for every Y[X]. In this paper, we show that universally right-stable spaces are just Hilbert spaces; every injective space is universally left-stable; a Banach space X isomorphic to a subspace of $ℓ_{∞}$ is universally left-stable if and only if it is isomorphic to $ℓ_{∞}$; and a separable space X has the property that (X,Y) is left-stable for every separable Y if and only if X is isomorphic to c₀.

Ograniczanie wyników

1 Studia Mathematica

1 Cheng L.

1 Dai D.

1 Dong Y.

1 Zhou Y.

1 2014

Wyniki wyszukiwania

Universal stability of Banach spaces for ε -isometries