DOI: 10.68381/jca18065 ISSN: 0944-6532
The Biduality Problem and M-Ideals in Weighted Spaces of Holomorphic Functions
Christopher Boyd, Pilar Rueda
Given a weight
v
v
on an open subset
U
U
of
{\bf C}^n
C
n
,
{\cal H}_v(U)
H
v
(
U
)
(resp.
{\cal H}_{v_o}(U)
H
v
o
(
U
)
) denotes the Banach space of holomorphic functions
f
f
on
U
U
such that
vf
v
f
is bounded on
U
U
(resp. converges to
0
0
on the boundary of
U
U
). We show that
{\cal H}_v(U)
H
v
(
U
)
is canonically isometrically isomorphic to the bidual of
{\cal H}_{v_o}(U)
H
v
o
(
U
)
if and only if
{\cal H}_{v_o}(U)
H
v
o
(
U
)
is an M-ideal in
{\cal H}_v(U)
H
v
(
U
)
and the associated weights
\tilde v_o
v
~
o
and
\tilde v
v
~
coincide