Please use this identifier to cite or link to this item: doi:10.22028/D291-30887
Title: Toeplitz operators on Hardy spaces
Author(s): Kraemer, Daniel
Language: English
Year of Publication: 2019
DDC notations: 510 Mathematics
Publikation type: Doctoral Thesis
Abstract: In the present thesis we establish Banach space counterparts for several results known for Toeplitz operators on Hardy-Hilbert spaces. We use methods of Didas, Eschmeier and Everard to construct Toeplitz projections for Toeplitz operators acting on a general class of Hardy-type spaces. These Toeplitz projections provide a general framework for Brown-Halmos type characterizations of Toeplitz operators and allow us to prove a Banach space version of a classical spectral inclusion theorem of Hartman and Wintner. Furthermore we show that a multivariable spectral mapping theorem of Eschmeier for Toeplitz tuples on Hardy-Hilbert spaces over strictly pseudoconvex domains with smooth boundary remains true in the corresponding Banach space setting. As an application we derive a spectral mapping theorem for truncated Toeplitz systems which generalizes a one dimensional result proved by Bessonov for the Hardy-Hilbert space on the unit disc.
Link to this record: urn:nbn:de:bsz:291--ds-308874
hdl:20.500.11880/29114
http://dx.doi.org/10.22028/D291-30887
Advisor: Eschmeier, Jörg
Date of oral examination: 24-Apr-2020
Date of registration: 11-May-2020
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Professorship: MI - Prof. Dr. Jörg Eschmeier
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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