Toeplitz operators on non-reflexive Fock spaces

Robert Fulsche ^[1]
1. [1] University of Hannover
  
  University of Hannover
  
  Region Hannover, Alemania
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 3, 2024, págs. 1115-1148
Idioma: inglés
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Resumen
- We generalize several results on Toeplitz operators over reflexive, standard weighted Fock spaces Ftp to the non-reflexive cases p=1,∞. Among these results are the characterization of compactness and the Fredholm property of such operators, a well-known representation of the Toeplitz algebra, and a characterization of the essential center of the Toeplitz algebra. Further, we improve several results related to correspondence theory, e.g., we improve previous results on the correspondence of algebras and we give a correspondence theoretic version of the well-known Berger–Coburn estimates.