The essential spectrum of Toeplitz tuples with symbols in H∞+C
Jörg Eschmeier
Studia Mathematica, Tome 215 (2013), p. 237-246 / Harvested from The Polish Digital Mathematics Library
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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 Tf=(Tf₁,...,Tfₘ)∈L(H²(σ))m with symbols fi∈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.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:285644 
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Jörg Eschmeier. The essential spectrum of Toeplitz tuples with symbols in $H^{∞} + C$
            . Studia Mathematica, Tome 215 (2013) pp. 237-246. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm219-3-4/