Proceedings of the American Mathematical Society

Asymptotically isometric copies of $\ell ^{\infty }$ in Banach spaces and a theorem of Bessaga and Pe $\l$ czynski

Author(s): Patrick N. Dowling; Narcisse Randrianantoanina
Journal: Proc. Amer. Math. Soc. 128 (2000), 3391-3397.
MSC (2000): Primary 46B20, 46B25
Posted: May 18, 2000
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We introduce the notion of a Banach space containing an asymptotically isometric copy of $\ell^\infty$ . A well known result of Bessaga and Pe $\l$ czynski states a Banach space

contains a complemented isomorphic copy of $\ell^1$ if and only if

contains an isomorphic copy of

if and only if

contains an isomorphic copy of $\ell^\infty$ . We prove an asymptotically isometric analogue of this result.

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Patrick N. Dowling
Affiliation: Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056
Email: pndowling@miavx1.muohio.edu

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