A proof of a necessary and sufficient condition for a sequence to be a multiplier of the normalized Haar basis of L¹[0,1] is given. This proof depends only on the most elementary properties of this system and is an alternative proof to that recently found by Semenov & Uksusov (2012). Additionally, representations are given, which use stochastic processes, of this multiplier norm and of related multiplier norms.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm227-2-4,
author = {H. M. Wark},
title = {A remark on the multipliers of the Haar basis of L$^1$[0,1]},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {141-148},
zbl = {06481149},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm227-2-4}
}
H. M. Wark. A remark on the multipliers of the Haar basis of L¹[0,1]. Studia Mathematica, Tome 231 (2015) pp. 141-148. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm227-2-4/