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On invariant domains in certain complex homogeneous spaces

Xiang-Yu Zhou — 1997

Annales de l'institut Fourier

Given a compact connected Lie group K . For a relatively compact K -invariant domain D in a Stein K -homogeneous space, we prove that the automorphism group of D is compact and if K is semisimple, a proper holomorphic self mapping of D is biholomorphic.

Linearization of isometric embedding on Banach spaces

Yu ZhouZihou ZhangChunyan Liu — 2015

Studia Mathematica

Let X,Y be Banach spaces, f: X → Y be an isometry with f(0) = 0, and T : s p a n ¯ ( f ( X ) ) X be the Figiel operator with T f = I d 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 s p a n ¯ ( f ( X ) ) is weakly nearly strictly convex.

Universal stability of Banach spaces for ε -isometries

Lixin ChengDuanxu DaiYunbai DongYu Zhou — 2014

Studia Mathematica

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 ) s p a n ¯ 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...

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