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On complemented versions of James's distortion theorems
Author(s):
William
B.
Johnson;
Narcisse
Randrianantoanina
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2751-2757.
MSC (2000):
Primary 46B20, 46B25:;
Secondary 46B03, 46B45
Posted:
March 30, 2007
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Abstract:
Examples are given to show that two natural questions asked in Dowling, Randrianantoanina, and Turett, 1999, about complemented versions of James's distortion theorems have negative answers.
References:
-
- 1.
- J. Diestel, Sequences and series in Banach spaces, Graduate Text in Mathematics, 92, Springer-Verlag, New York, 1984. MR 0737004 (85i:46020)
- 2.
- S. Dilworth, M. Girardi, and J. Hagler, Dual Banach spaces which contain an isometric copy of
 , Bull. Polish Acad. Sci. Math. 48 (2000), 1-12. MR 1751149 (2001e:46016) - 3.
- P. N. Dowling, Isometric copies of
 and  in duals of Banach spaces, J. Math. Anal. Appl. 244 (2000), no. 1, 223-227. MR 1746799 (2000m:46036) - 4.
- P. N. Dowling, W. B. Johnson, C. J. Lennard, and B. Turett, The optimality of James's distortion theorems, Proc. Amer. Math. Soc. 125 (1997), no. 1, 167-174. MR 1346969 (97d:46010)
- 5.
- P. N. Dowling, N. Randrianantoanina, and B. Turett, Remarks on James's distortion theorems. II, Bull. Austral. Math. Soc. 59 (1999), no. 3, 515-522. MR 1698052 (2000c:46022)
- 6.
- M. Fabian, P. Habala, P. Hájek, V. Montesinos Santalucía, J. Pelant, and V. Zizler, Functional analysis and infinite-dimensional geometry, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 8, Springer-Verlag, New York, 2001. MR 1831176 (2002f:46001)
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Additional Information:
William
B.
Johnson
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email:
johnson@math.tamu.edu
Narcisse
Randrianantoanina
Affiliation:
Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056
Email:
randrin@muohio.edu
DOI:
10.1090/S0002-9939-07-08775-8
PII:
S 0002-9939(07)08775-8
Keywords:
$\ell_1$,
$c_0$,
renorming,
James's distortion theorems
Received by editor(s):
January 10, 2006
Received by editor(s) in revised form:
May 1, 2006
Posted:
March 30, 2007
Additional Notes:
The first author's research was partially supported by NSF DMS--0503688
The second author's research was partially supported by NSF DMS--0456781.
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2007,
by the authors
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