Smooth Approximation of Lipschitz Projections
نویسنده
چکیده
We show that any Lipschitz projection-valued function p on a connected closed Riemannian manifold can be approximated uniformly by smooth projection-valued functions q with Lipschitz constant close to that of p. This answers a question of Rieffel.
منابع مشابه
Smooth Approximations
We prove that a Lipschitz (or uniformly continuous) mapping f : X → Y can be approximated by smooth Lipschitz (resp. uniformly continuous) mapping, if X is a separable Banach space admitting a smooth Lipschitz bump and either X or Y is a C(K) space (resp. super-reflexive space). As a corollary we obtain also smooth approximation of C1-smooth mappings together with their first derivatives.
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