A compact set without Markov's property but with an extension operator for $C^∞$-functions
Volume 119 / 1996
Studia Mathematica 119 (1996), 27-35
DOI: 10.4064/sm-119-1-27-35
Abstract
We give an example of a compact set K ⊂ [0, 1] such that the space ℇ(K) of Whitney functions is isomorphic to the space s of rapidly decreasing sequences, and hence there exists a linear continuous extension operator $L: ℇ(K) → C^{∞}[0,1]$. At the same time, Markov's inequality is not satisfied for certain polynomials on K.
