论文标题
在Lipschitz运算符上理想$ \ text {lip} _ {0} \ circ \ mathcal a \ circ \ circ \ text {lip} _ {0} $
On the Lipschitz operator ideal $\text{Lip}_{0}\circ \mathcal A\circ \text{Lip}_{0}$
论文作者
论文摘要
我们研究一种系统的方法，从Banach线性操作员理想$ \ Mathcal a $中生产Lipschitz运营商理想。对于最大和最小操作员的理想，分别研究了Lipschitz的最大船体和Lipschitz操作员理想的最小内核$ \ text {lip} _0 \ circ \ mathcal a \ mathcal a \ circ \ circ \ circ \ circ \ circ \ text {lip} _0 $。使用超级副作用技术，我们获得了Kürsten和Piestch结果的Lipschitz版本，这些版本表征了所有Lipschitz操作员理想的最大船体。除其他结果外，我们表征了属于$ \ text {lip} _0 \ circ \ mathcal a \ circ \ circ \ text {lip} _0 $的线性运算符，在许多情况下，它们正是$ \ Mathcal a $ a $ a $。特别是，我们给出了某些情况，在某些情况下，就给定的Banach线性操作员理想$ \ Mathcal a $而言，线性运算符的非线性分解意味着线性。
We study a systematic way to produce a Lipschitz operator ideal from a Banach linear operator ideal $\mathcal A$. For maximal and minimal operator ideals $\mathcal A$, the Lipschitz maximal hull and minimal kernel of the Lipschitz operator ideals $\text{Lip}_0 \circ \mathcal A \circ \text{Lip}_0$ are investigated, respectively. Using ultraproduct techniques, we obtain the Lipschitz version of a result of Kürsten and Piestch which characterizes the maximal hull of any Lipschitz operator ideal. Among other results, we characterize the linear operators which belong to $\text{Lip}_0\circ \mathcal A\circ \text{Lip}_0$ which, in many cases, they are precisely those which are in $\mathcal A$. In particular, we give some cases in which a nonlinear factorization of linear operators implies a linear one, in terms of a given Banach linear operator ideal $\mathcal A$.
