A note on certain partial sum operators

@article{MarekBożejko2006,
abstract = {We show that for the t-deformed semicircle measure, where 1/2 < t ≤ 1, the expansions of $L_p$ 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 $L_p$ spaces of free group factors and of free commutation relations do not converge for 1 ≤ p < 3/2 or 3 < p.},
author = {Marek Bożejko, Gero Fendler},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {117-225},
title = {A note on certain partial sum operators},
url = {http://eudml.org/doc/282148},
volume = {73},
year = {2006},
}

TY - JOUR
AU - Marek Bożejko
AU - Gero Fendler
TI - A note on certain partial sum operators
JO - Banach Center Publications
PY - 2006
VL - 73
IS - 1
SP - 117
EP - 225
AB - We show that for the t-deformed semicircle measure, where 1/2 < t ≤ 1, the expansions of $L_p$ 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 $L_p$ spaces of free group factors and of free commutation relations do not converge for 1 ≤ p < 3/2 or 3 < p.
LA - eng
UR - http://eudml.org/doc/282148
ER -