The essential spectrum of Toeplitz tuples with symbols in $H^{∞} + C$

• Autorzy: Jörg Eschmeier
• Języki publikacji: EN

Abstrakty

EN

Let H²(D) be the Hardy space on a bounded strictly pseudoconvex domain D ⊂ ℂⁿ with smooth boundary. Using Gelfand theory and a spectral mapping theorem of Andersson and Sandberg (2003) for Toeplitz tuples with $H^{∞}$-symbol, we show that a Toeplitz tuple $T_{f} = (T_{f₁}, ..., T_{fₘ}) ∈ L(H²(σ))^{m}$ with symbols $f_{i} ∈ H^{∞} + C$ is Fredholm if and only if the Poisson-Szegö extension of f is bounded away from zero near the boundary of D. Corresponding results are obtained for the case of Bergman spaces. Thus we extend results of McDonald (1977) and Jewell (1980) to systems of Toeplitz operators.

Kategorie tematyczne

• 47A53: (Semi-) Fredholm operators; index theories
• 47A13: Several-variable operator theory (spectral, Fredholm, etc.)
• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 219
• Numer: 3
• Strony: 237-246

Daty

wydano

2013

Twórcy

autor

Jörg Eschmeier

• Fachrichtung Mathematik, Universität des Saarlandes, D-66041 Saarbrücken, Germany

Identyfikatory

DOI

10.4064/sm219-3-4