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Fredholm theory of Toeplitz operators on standard weighted Fock spaces

Al-qabani, A. and Virtanen, J. (2018) Fredholm theory of Toeplitz operators on standard weighted Fock spaces. Annales Academiæ Scientiarum Fennicæ Mathematica, 43. pp. 769-783. ISSN 1798-2383

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To link to this item DOI: 10.5186/aasfm.2018.4344

Abstract/Summary

We study the Fredholm properties of Toeplitz operators with bounded symbols of vanishing mean oscillation in the complex plane. In particular, we prove that the Toeplitz operator with such a symbol is Fredholm on a standard weighted Fock space if and only if the Berezin transform of the symbol is bounded away from zero outside a sufficiently large disk in the complex plane. We also show that the Fredholm index of the Toeplitz operator can be computed via the winding of the symbol along a sufficiently large circle. We finish by considering Toeplitz operators with matrix-valued symbols.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:75937
Publisher:Academia Scientiarum Fennica

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