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arXiv · 1211.0783

Simultaneous generic approximation by the iterates of the Cesaro operator

Theodosios Douvropoulos
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Abstract

We show that for the generic sequence (a) of elements in a subset A of a separable locally convex metrisable space V, the sequences [T^k(a)]_n, n=1,2,... are dense in the convex hull convA of A for all k=1,2,...; where T is the Cesaro operator. Further, if convA is dense in V, then for every sequence x_k of elements of V, k=1,2,... there exists a sequence of indices l_n, n=1,2,..., such that, we have the simultaneous approximation that [T^k(a)]_(l_n) converges to x_k as n tends to infinity for all k=1,2,... These phenomena are topologically generic and in the case where A is a vector space they are algebraically generic.

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Theodosios Douvropoulos. 2012-11-05. Simultaneous generic approximation by the iterates of the Cesaro operator. https://arxiv.org/abs/1211.0783

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