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.

中文翻译：

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Banach空间的张量范数和算子理想的近似性质

摘要 对于有限生成的张量范数 α \alpha ，我们研究了 α \alpha -approximation property ( α \alpha -AP) 和有界 α \alpha -approximation property (bounded α \alpha -AP) 的一些近似性质运营商的理想。我们证明 Banach 空间 X 具有 λ \lambda 有界 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) 如果它有 λ \lambda 有界 gp {g}_{p} -AP。因此，如果 Banach 空间 X 具有 λ \lambda -bounded gp {g}_{p} -AP，则 X 具有 λ \lambda -bounded wp {w}_{p} -AP。