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ISSN 1088-6826(e) ISSN 0002-9939(p)

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
MathSciNet review: 1690984
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Abstract | References | Similar articles | Additional information

Abstract:

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.

References:

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Additional Information:

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

Narcisse Randrianantoanina
Affiliation: Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056
Email: randrin@muohio.edu

DOI: 10.1090/S0002-9939-00-05447-2
PII: S 0002-9939(00)05447-2
Received by editor(s): June 26, 1998
Received by editor(s) in revised form: January 22, 1999
Posted: May 18, 2000
Additional Notes: The second author was supported in part by a Miami University Summer Research Appointment and by NSF grant DMS-9703789.
Communicated by: Dale Alspach
Copyright of article: Copyright 2000, American Mathematical Society

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