Bounded below composition operators on the space of Bloch functions on the unit ball of a Hilbert space
Let B E be the open unit ball of a complex finite or infinite dimensional Hilbert space E and consider the space B ( B E ) of Bloch functions on B E . Using Lipschitz continuity of the dilation map on B E given by x ↦ ( 1 - ‖ x ‖ 2 ) R f ( x ) for x ∈ B E , where R f denotes the radial derivative of...
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| Vydáno v: | Banach journal of mathematical analysis Ročník 17; číslo 4 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Cham
Springer International Publishing
01.10.2023
|
| Témata: | |
| ISSN: | 2662-2033, 1735-8787 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | Let
B
E
be the open unit ball of a complex finite or infinite dimensional Hilbert space
E
and consider the space
B
(
B
E
)
of Bloch functions on
B
E
. Using Lipschitz continuity of the dilation map on
B
E
given by
x
↦
(
1
-
‖
x
‖
2
)
R
f
(
x
)
for
x
∈
B
E
, where
R
f
denotes the radial derivative of
f
∈
B
(
B
E
)
, we study when a composition operator on
B
(
B
E
)
is bounded below. |
|---|---|
| ISSN: | 2662-2033 1735-8787 |
| DOI: | 10.1007/s43037-023-00295-w |