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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
)
.