### Greedy Approximation in Certain Subsystems of the Schauder System

M. G. Grigoryan, A. A. Sargsyan, and R. E. Zink
Source: Real Anal. Exchange Volume 34, Number 1 (2008), 227-238.

#### 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.

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Primary Subjects: 42C10
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Permanent link to this document: http://projecteuclid.org/euclid.rae/1242738934
Zentralblatt MATH identifier: 05578228
Mathematical Reviews number (MathSciNet): MR2527136

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