We construct two compact Hausdorff spaces,
X
X
and
Y
Y
, so that
C
(
X
)
C(X)
does not embed isometrically into
C
(
Y
)
C(Y)
, but for each
ε
>
0
\varepsilon > 0
, there is an isomorphism
T
ε
{T_\varepsilon }
from
C
(
X
)
C(X)
into
C
(
Y
)
C(Y)
satisfying
∥
f
∥⩽∥
T
ε
f
∥⩽
(
1
+
ε
)
∥
f
∥
\parallel f\parallel \leqslant \parallel {T_\varepsilon }f\;\parallel \leqslant (1 + \varepsilon )\parallel f\parallel
for all
f
∈
C
(
X
)
f \in C(X)
.