We show that for the t-deformed semicircle measure, where 1/2 < t ≤ 1, the expansions of functions with respect to the associated orthonormal polynomials converge in norm when 3/2 < p < 3 and do not converge when 1 ≤ p < 3/2 or 3 < p. From this we conclude that natural expansions in the non-commutative spaces of free group factors and of free commutation relations do not converge for 1 ≤ p < 3/2 or 3 < p.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-7,
author = {Marek Bo\.zejko and Gero Fendler},
title = {A note on certain partial sum operators},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {117-225},
zbl = {1109.46051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-7}
}
Marek Bożejko; Gero Fendler. A note on certain partial sum operators. Banach Center Publications, Tome 72 (2006) pp. 117-225. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc73-0-7/