A note on certain partial sum operators

Tom 73 / 2006

Marek Bożejko, Gero Fendler Banach Center Publications 73 (2006), 117-225 MSC: Primary 46L51; Secondary 42C10. DOI: 10.4064/bc73-0-7

Streszczenie

We show that for the $t$-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 $3< p$.

Autorzy

  • Marek BożejkoInstytut Matematyczny
    Uniwersytet Wroc/lawski
    Plac Grunwaldzki 2/4
    50-384 Wroc/law, Poland
    e-mail
  • Gero FendlerFinstertal 16
    D-69514 Laudenbach, Germany
    e-mail

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