Three-space problems for the bounded compact approximation property

History, Developments and Open Problems on Approximation Properties

“…The pair (X, X) has the λ-BAP if and only if X has the λ-BAP [12]. This notion was first extended to the bounded compact approximation property for pairs by Chen and Zheng [29]. Then Chen, Kim and Zheng [28] defined a weaker notion of the bounded approximation property of pairs.…”

Type, cotype and twisted sums induced by complex interpolation

“…But by taking constant functions θ j (y j , 0) ≤ 9 1− 1 p θ j y j Yp So replacing z i by zi and z * i by z * i , we can reproduce the proof that Y p does not have the CAP to F /(ker(δ θ ) ∩ ker(δ ′ θ )). For more on twisted sums involving the approximation property, see for example [15], [16], [22] and [42].…”