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), 33913397
MSC (2000):
Primary 46B20, 46B25
Published electronically:
May 18, 2000
MathSciNet review:
1690984
Fulltext PDF Free Access
Abstract 
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Abstract: 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:
http://dx.doi.org/10.1090/S0002993900054472
PII:
S 00029939(00)054472
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 DMS9703789.
Communicated by:
Dale Alspach
Article copyright:
© Copyright 2000
American Mathematical Society
