Details

Autor(en) / Beteiligte

• Dewage, Vishwa
• Ólafsson, Gestur

Titel

Toeplitz Operators on the Fock Space with Quasi-Radial Symbols

Ist Teil von

• Complex analysis and operator theory, 2022-06, Vol.16 (4), Article 61

Ort / Verlag

Cham: Springer International Publishing

Erscheinungsjahr

2022

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• The Fock space F ( C n ) is the space of holomorphic functions on C n that are square-integrable with respect to the Gaussian measure on C n . This space plays an important role in several subfields of analysis and representation theory. In particular, it has for a long time been a model to study Toeplitz operators. Esmeral and Maximenko showed in 2016 that radial Toeplitz operators on F ( C ) generate a commutative C ∗ -algebra which is isometrically isomorphic to the C ∗ -algebra C b , u ( N 0 , ρ 1 ) . In this article, we extend the result to k -quasi-radial symbols acting on the Fock space F ( C n ) . We calculate the spectra of the said Toeplitz operators and show that the set of all eigenvalue functions is dense in the C ∗ -algebra C b , u ( N 0 k , ρ k ) of bounded functions on N 0 k which are uniformly continuous with respect to the square-root metric. In fact, the C ∗ -algebra generated by Toeplitz operators with quasi-radial symbols is C b , u ( N 0 k , ρ k ) .