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

Jörg Eschmeier. "The essential spectrum of Toeplitz tuples with symbols in $H^{∞} + C$." Studia Mathematica 219.3 (2013): 237-246. <http://eudml.org/doc/285644>.

@article{JörgEschmeier2013,
abstract = {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.},
author = {Jörg Eschmeier},
journal = {Studia Mathematica},
language = {eng},
number = {3},
pages = {237-246},
title = {The essential spectrum of Toeplitz tuples with symbols in $H^\{∞\} + C$},
url = {http://eudml.org/doc/285644},
volume = {219},
year = {2013},
}

TY - JOUR
AU - Jörg Eschmeier
TI - The essential spectrum of Toeplitz tuples with symbols in $H^{∞} + C$
JO - Studia Mathematica
PY - 2013
VL - 219
IS - 3
SP - 237
EP - 246
AB - 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.
LA - eng
UR - http://eudml.org/doc/285644
ER -