Abstract
For a finitely generated tensor norm
α
\alpha
, we investigate the
α
\alpha
-approximation property (
α
\alpha
-AP) and the bounded
α
\alpha
-approximation property (bounded
α
\alpha
-AP) in terms of some approximation properties of operator ideals. We prove that a Banach space X has the
λ
\lambda
-bounded
α
p
,
q
{\alpha }_{p,q}
-AP
(
1
≤
p
,
q
≤
∞
,
1
/
p
+
1
/
q
≥
1
)
(1\le p,q\le \infty ,1/p+1/q\ge 1)
if it has the
λ
\lambda
-bounded
g
p
{g}_{p}
-AP. As a consequence, it follows that if a Banach space X has the
λ
\lambda
-bounded
g
p
{g}_{p}
-AP, then X has the
λ
\lambda
-bounded
w
p
{w}_{p}
-AP.
The Lipschitz bounded approximation property for operator ideals
