Asymptotically isometric copies of in Banach spaces and a theorem of Bessaga and Peczynski

Authors:
Patrick N. Dowling and Narcisse Randrianantoanina

Journal:
Proc. Amer. Math. Soc. **128** (2000), 3391-3397

MSC (2000):
Primary 46B20, 46B25

DOI:
https://doi.org/10.1090/S0002-9939-00-05447-2

Published electronically:
May 18, 2000

MathSciNet review:
1690984

Full-text PDF

Abstract | References | Similar Articles | Additional Information

We introduce the notion of a Banach space containing an asymptotically isometric copy of . A well known result of Bessaga and Peczynski states a Banach space contains a complemented isomorphic copy of if and only if contains an isomorphic copy of if and only if contains an isomorphic copy of . We prove an asymptotically isometric analogue of this result.

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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:
https://doi.org/10.1090/S0002-9939-00-05447-2

Received by editor(s):
June 26, 1998

Received by editor(s) in revised form:
January 22, 1999

Published electronically:
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

Article copyright:
© Copyright 2000
American Mathematical Society