Year: 2012
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Douvropoulos, Theodosios
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2298402257