A note on certain partial sum operators
Volume 73 / 2006
Banach Center Publications 73 (2006), 117-225
MSC: Primary 46L51; Secondary 42C10.
DOI: 10.4064/bc73-0-7
Abstract
We show that for the -deformed semicircle measure, where \frac{1}{2}< t\leq 1, the expansions of L_p functions with respect to the associated orthonormal polynomials converge in norm when \frac{3}{2}< p< 3 and do not converge when 1\leq p< \frac{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\leq p< \frac{3}{2} or 3< p.
