Geodesic
SOME RESULTS OF THE $\mathcal K_{\mathcal A}$-APPROXIMATION PROPERTY FOR BANACH SPACES
Glasgow mathematical journal, Tome 61 (2019) no. 3, pp. 545-555

Voir la notice de l'article provenant de la source Cambridge University Press

Given a Banach operator ideal $\mathcal A$, we investigate the approximation property related to the ideal of $\mathcal A$-compact operators, $\mathcal K_{\mathcal A}$-AP. We prove that a Banach space X has the $\mathcal K_{\mathcal A}$-AP if and only if there exists a λ ≥ 1 such that for every Banach space Y and every R ∈ $\mathcal K_{\mathcal A}$(Y, X),$$\begin{equation}R \in \overline {\{SR : S \in \mathcal F(X, X), \|SR\|_{\mathcal K_{\mathcal A}} \leq \lambda \|R\|_{\mathcal K_{\mathcal A}}\}}^{\tau_{c}}.\end{equation}$$For a surjective, maximal and right-accessible Banach operator ideal $\mathcal A$, we prove that a Banach space X has the $\mathcal K_{(\mathcal A^{{\rm adj}})^{{\rm dual}}}$-AP if the dual space of X has the $\mathcal K_{\mathcal A}$-AP. 
KIM, JU MYUNG. SOME RESULTS OF THE $\mathcal K_{\mathcal A}$-APPROXIMATION PROPERTY FOR BANACH SPACES. Glasgow mathematical journal, Tome 61 (2019) no. 3, pp. 545-555. doi: 10.1017/S0017089518000356
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