Failure of Nehari's theorem for multiplicative Hankel forms in Schatten classes

• Autorzy: Ole Fredrik Brevig , Karl-Mikael Perfekt
• Języki publikacji: EN

Abstrakty

EN

Ortega-Cerdà-Seip demonstrated that there are bounded multiplicative Hankel forms which do not arise from bounded symbols. On the other hand, when such a form is in the Hilbert-Schmidt class 𝓢₂, Helson showed that it has a bounded symbol. The present work investigates forms belonging to the Schatten classes between these two cases. It is shown that for every $p > (1- log π/log 4)^{-1}$ there exist multiplicative Hankel forms in the Schatten class $𝓢_{p}$ which lack bounded symbols. The lower bound on p is in a certain sense optimal when the symbol of the multiplicative Hankel form is a product of homogeneous linear polynomials.

Kategorie tematyczne

• 30B50: Dirichlet series and other series expansions, exponential series
• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 228
• Numer: 2
• Strony: 101-108

Daty

wydano

2015

Twórcy

autor

Ole Fredrik Brevig

• Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway

autor

Karl-Mikael Perfekt

• Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norway

Identyfikatory

DOI

10.4064/sm228-2-1