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Commutators of weighted Hardy operators on Herz-type spaces

100%
Tang C., Xue F., Zhou Y.
Annales Polonici Mathematici
|
2011
|
tom 101
|
nr 3
267-273
EN
A sufficient condition for boundedness on Herz-type spaces of the commutator generated by a Lipschitz function and a weighted Hardy operator is obtained.
2
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Universal stability of Banach spaces for ε -isometries

100%
Cheng L., Dai D., Dong Y., Zhou Y.
Studia Mathematica
|
2014
|
tom 221
|
nr 2
141-149
EN
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.
3
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Linearization of isometric embedding on Banach spaces

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Zhou Y., Zhang Z., Liu C.
Studia Mathematica
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2015
|
tom 230
|
nr 1
31-39
EN
Let X,Y be Banach spaces, f: X → Y be an isometry with f(0) = 0, and $T: \overline{span}(f(X)) → X$ be the Figiel operator with $T ∘ f = Id_{X}$ and ||T|| = 1. We present a sufficient and necessary condition for the Figiel operator T to admit a linear isometric right inverse. We also prove that such a right inverse exists when $\overline{span}(f(X))$ is weakly nearly strictly convex.
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