Abstract
Although the sequence of greedy approximants associated with the Schauder expansion of a function, $f$, continuous on $[0,1]$, may fail to converge, there always will be a continuous function, arbitrarily close to $f$, whose Schauder expansion does have a convergent sequence of greedy approximants. Further examination of this problem shows that the same sort of proposition is valid for a multitude of subsystems of the Schauder system.
Citation
M. G. Grigoryan. A. A. Sargsyan. R. E. Zink. "Greedy Approximation in Certain Subsystems of the Schauder System." Real Anal. Exchange 34 (1) 227 - 238, 2008/2009.
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