Toeplitz operators and generated algebras on non-Hilbertian spaces

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dc.identifier.uri Fulsche, Robert ger 2020-12-02T13:18:44Z 2020-12-02T13:18:44Z 2020
dc.identifier.citation Fulsche, Robert: Toeplitz operators and generated algebras on non-Hilbertian spaces. Hannover : Gottfried Wilhelm Leibniz Universität, Diss., 2020, viii, 198 S. DOI: ger
dc.description.abstract In this thesis we study Toeplitz operators on spaces of holomorphic and pluriharmonic functions. The main part of the thesis is concerned with such operators on the p-Fock spaces of holomorphic functions for p ∈ [1, ∞]. We establish a notion of Correspondence Theory between symbols and Toeplitz operators, based on extended notions of convolutions as developed by Reinhard Werner, which gives rise to many important results on Toeplitz operators and the algebras they generate. Here, we find new proofs for old theorems, extending them to a larger range of values of p, and also provide entirely new results. We manage to include even the non-reflexive cases of p = 1, ∞ in our studies. Based on the notions of band-dominated and limit operators, we establish a general criterion for an operator in the Toeplitz algebra over the Fock space to be Fredholm: Such an operator is Fredholm if and only if all of its limit operators are invertible. As an example of a Toeplitz algebra over the Fock space, we study the Resolvent Algebra (in the sense of Detlev Buchholz and Hendrik Grundling) in its Fock space representation. Partially following the methods of Correspondence Theory as discussed in this thesis, we manage to extend a classical result on the boundedness of Toeplitz operators (the Berger-Coburn estimates) to the setting of p-Fock spaces. Also based on results derived from the Correspondence Theory, we discuss several new characterizations of the full Toeplitz algebra on Fock spaces, at least in the reflexive range p ∈ (1, ∞). In the last part, we discuss several results on spectral theory and quantization estimates for Toeplitz operators acting on Bergman and Fock spaces of pluriharmonic functions. eng
dc.language.iso eng ger
dc.publisher Hannover : Institutionelles Repositorium der Leibniz Universität Hannover
dc.rights Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. ger
dc.subject Toeplitz operators eng
dc.subject Fock space eng
dc.subject operator algebras eng
dc.subject Toeplitzoperatoren ger
dc.subject Fockraum ger
dc.subject Operatoralgebren ger
dc.subject.ddc 510 | Mathematik ger
dc.title Toeplitz operators and generated algebras on non-Hilbertian spaces eng
dc.type doctoralThesis ger
dc.type Text ger
dc.description.version publishedVersion ger
tib.accessRights frei zug�nglich ger

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