Fredholm theory of Toeplitz operators on standard weighted Fock spaces

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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 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.

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Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/75937
Identification Number/DOI	10.5186/aasfm.2018.4344
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Academia Scientiarum Fennica
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Funders:	Engineering and Physical Sciences Research Council	The sponsoring bodies who contributed funding for the creation of this item. Example: NERC Example: The Royal Society of Chemistry A pick list of funders may appear as you type in the funder's name in full or as an acronym. Select a correct match to complete the field or type in a new entry in full. For new entries, the full name is preferred.
Projects:	Riemann-Hilbert problems, infinite matrices and their applications Funded by: Engineering and Physical Sciences Research Council (EP/M024784/1 - £98,560) Project Lead: Jani A. Virtanen Local Lead (PI): Jani Virtanen 1 June 2015 - 31 May 2017	Click Add to select your project (received at Reading) from an autocomplete list.

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Date Deposited:	16 Mar 2018 15:27	Date item deposited into CentAUR
Last Modified:	23 Mar 2025 02:21	Date item last modified

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