The strong approximation property and the weak bounded approximation property |
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| Authors: | Ju Myung Kim Bentuo Zheng |
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| Institution: | 1. Department of Mathematical Sciences, Seoul National University, Seoul 151-742, Republic of Korea;2. Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152-3240, United States |
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| Abstract: | 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. This gives a negative answer to Oja's conjecture. As a consequence, we show that each of the spaces c0 and ?1 has a subspace which has the AP but fails to have the strong AP. |
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| Keywords: | Approximation property Strong approximation property Weak bounded approximation property Bounded approximation property |
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