Three-space problems for the bounded compact approximation property
In this paper, the notion of the bounded compact approximation property (BCAP) of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of L∞ with the BCAP, then L∞/X has the BCAP. We also show that X* has the λ-BCAP with conjugate operators if and only if the pair (X, Y) has the λ-BCAP for each finite codimensional subspace Y ⊆ X. Let M be a closed subspace of X such that M⊥ is complemented in X*. If X has the (bounded) approximation property of order p, then M has the (bounded) approximation property of order p. © 2013 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg.
Acta Mathematica Sinica, English Series
Chen, D., & Zheng, B. (2013). Three-space problems for the bounded compact approximation property. Acta Mathematica Sinica, English Series, 29 (4), 625-632. https://doi.org/10.1007/s10114-012-0661-7