A note on certain partial sum operators

• Autorzy: Marek Bożejko , Gero Fendler
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46L51: Noncommutative measure and integration
• 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2006
• Tom: 73
• Numer: 1
• Strony: 117-225

Daty

wydano

2006

Twórcy

autor

Marek Bożejko

• Instytut Matematyczny, Uniwersytet Wrocławski, Plac Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Gero Fendler

• Finstertal 16, D-69514 Laudenbach, Germany

Identyfikatory

DOI

10.4064/bc73-0-7