We show that the strong approximation property (strong AP) (respectively, strong CAP) and the weak bounded approximation property (respectively, weak BCAP) are equivalent for every Banach space.
Let (x^) and (y^) be respectively weak cluster points of the sequences ({x_{n}}) and ({y_{n}} ).
We denote by (x_{n} rightarrow x) (respectively, (x_{n}rightharpoonup x)) the strong (respectively, weak) convergence of the sequence ({x_{n}}) to x.
When {x n } is a sequence in E, x n → x (x n ⇀ x, x n ⇁ x) will denote strong (respectively, weak and weak*) convergence of the sequence {x n } to x.
The compactness of cl ( T ( M p ) ) (respectively, weak compactness of wcl ( T ( M p ) ) ) implies that cl ( T ( D ) ) is compact (respectively, wcl ( T ( D ) ) is weakly compact).
Let {x n } be a sequence in H1, then x n →x (respectively, x n ⇀ x Open image in new window) denotes strong (respectively, weak) convergence of the sequence {x n } to a point x∈H1.
We present some technical lemmas which are crucial in the proof of the Theorem 1.2 in Section 3. Theorem 1.2 is proved in Section 4. Throughout this article, C, C i will denote various positive constants whose exact values are not important, → (respectively ⇀) denotes strong (respectively weak) convergence.
Then T is said to be demiclosed at v ∈ H if, for any sequence {x n } in C, the following implication holds: x n ⇀ u ∈ C, T x n → v imply T u = v, where → (respectively ⇀) denotes strong (respectively weak) convergence.
Because the F-statistics for the Medicare Wage Index and general overhead per day were 23.69 and 58.91, respectively, weak correlation is unlikely to be a source of bias (Bound, Jaeger, and Baker 1995; Staiger and Stock 1994).
