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The Bishop–Phelps–Bollobás Property for Weighted Holomorphic Mappings
Given an open subset U of a complex Banach space E , a weight v on U and a complex Banach space F , let H v ∞ ( U , F ) denote the Banach space of all weighted holomorphic mappings from U into F , endowed with the weighted supremum norm. We introduce and study a version of the Bishop–Phelps–Bollobás...
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| Published in: | Resultate der Mathematik 2024-06, Vol.79 (4), Article 155 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites |
| Online Access: | Get full text |
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| Summary: | Given an open subset
U
of a complex Banach space
E
, a weight
v
on
U
and a complex Banach space
F
, let
H
v
∞
(
U
,
F
)
denote the Banach space of all weighted holomorphic mappings from
U
into
F
, endowed with the weighted supremum norm. We introduce and study a version of the Bishop–Phelps–Bollobás property for
H
v
∞
(
U
,
F
)
(
W
H
∞
-BPB property, for short). A result of Lindenstrauss type with sufficient conditions for
H
v
∞
(
U
,
F
)
to have the
W
H
∞
-BPB property for every space
F
is stated. This is the case of
H
v
p
∞
(
D
,
F
)
with
p
≥
1
, where
v
p
is the standard polynomial weight on
D
. The study of the relations of the
W
H
∞
-BPB property for the complex and vector-valued cases is also addressed as well as the extension of the cited property for mappings
f
∈
H
v
∞
(
U
,
F
)
such that
vf
has a relatively compact range in
F
. |
|---|---|
| ISSN: | 1422-6383 1420-9012 |
| DOI: | 10.1007/s00025-024-02184-6 |