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(Solved): Please answer the following functional analysis question: Let Y be a closed subspace of a Banach spa ...
Please answer the following functional analysis question:
Let
Y
be a closed subspace of a Banach space
X
,
y
∈
/
Y
,
L
=
y
+
Y
,
x
∈
/
L
. Show that there exists
f
∈
X
∗
such that
f
(
x
)
=
f
(
z
)
for every
z
∈
L
.
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