Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 12 (2005) no. 1, pp. 103-106
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Vladimir Kadets. The Haar system in $L_1$ is monotonically boundedly complete. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 12 (2005) no. 1, pp. 103-106. http://geodesic.mathdoc.fr/item/JMAG_2005_12_1_a5/
@article{JMAG_2005_12_1_a5,
author = {Vladimir Kadets},
title = {The {Haar} system in $L_1$ is monotonically boundedly complete},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {103--106},
year = {2005},
volume = {12},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JMAG_2005_12_1_a5/}
}
TY - JOUR
AU - Vladimir Kadets
TI - The Haar system in $L_1$ is monotonically boundedly complete
JO - Žurnal matematičeskoj fiziki, analiza, geometrii
PY - 2005
SP - 103
EP - 106
VL - 12
IS - 1
UR - http://geodesic.mathdoc.fr/item/JMAG_2005_12_1_a5/
LA - en
ID - JMAG_2005_12_1_a5
ER -
%0 Journal Article
%A Vladimir Kadets
%T The Haar system in $L_1$ is monotonically boundedly complete
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2005
%P 103-106
%V 12
%N 1
%U http://geodesic.mathdoc.fr/item/JMAG_2005_12_1_a5/
%G en
%F JMAG_2005_12_1_a5
Answering a question posed by J. R. Holub we show that for the normalized Haar system $\{h_n\}$ in $L_1[0,1]$ whenever $\{a_n\}$ is a sequence of scalars with $|a_n|$ decreasing monotonically and with $\sup_N\|\sum_{n=1}^N a_n h_n\| < \infty$, then $ \sum_{n=1}^\infty a_n h_n$ converges in $L_1[0,1]$.
