## Addendum to “Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces" (Colloq. Math. 127 (2012), 105–109)

### Volume 137 / 2014

Colloquium Mathematicum 137 (2014), 297-298
MSC: Primary 46E30, 46B15; Secondary 46B25.
DOI: 10.4064/cm137-2-12

#### Abstract

It is well known that if $\varphi (t) \equiv t $, then the system $ \{ \varphi ^{n}(t)\}_{n=0}^{\infty }$ is not a Schauder basis in $ L_{2}[0,1] $. It is natural to ask whether there is a function $\varphi $ for which the power system $ \{ \varphi ^{n}(t)\}_{n=0}^{\infty }$ is a basis in some Lebesgue space $L_{p}$. The aim of this short note is to show that the answer to this question is negative.