Abstract
AbstractGeneralized multipliers for a left-invertible operator T, whose formal Laurent series $$U_x(z)=\sum _{n=1}^\infty (P_ET^{n}x)\frac{1}{z^n}+\sum _{n=0}^\infty (P_E{T^{\prime *n}}x)z^n$$
U
x
(
z
)
=
∑
n
=
1
∞
(
P
E
T
n
x
)
1
z
n
+
∑
n
=
0
∞
(
P
E
T
′
∗
n
x
)
z
n
, $$x\in \mathcal {H}$$
x
∈
H
actually represent analytic functions on an annulus or a disc are investigated. We show that they are coefficients of analytic functions and characterize the commutant of some left-invertible operators, which satisfies certain conditions in its terms. In addition, we prove that the set of multiplication operators associated with a weighted shift on a rootless directed tree lies in the closure of polynomials in z and $$\frac{1}{z}$$
1
z
of the weighted shift in the topologies of strong and weak operator convergence.
Funder
Jagiellonian University in Krakow
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference27 articles.
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3. Budzyński, P., Dymek, P., Ptak, M.: Analytic structure of weighted shifts on directed trees. Math. Nachrichten 290, 1612–1629 (2016)
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5. Budzyński, P., Jabłoński, Z.J., Jung, I.B., Stochel, J.: Subnormal weighted shifts on directed trees whose $$n$$-th powers have trivial domain. J. Math. Anal. Appl. 435, 302–314 (2016)
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