Complemented isometric copies of in dual Banach spaces
Author:
J. Hagler
Journal:
Proc. Amer. Math. Soc. 130 (2002), 33133324
MSC (2000):
Primary 46B04, 46B10; Secondary 46B20
Published electronically:
March 25, 2002
MathSciNet review:
1913011
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Let be a real or complex Banach space and . Then contains a complemented, isometric copy of if and only if contains a complemented, isometric copy of if and only if contains a subspace asymptotic to .
 [DGH]
S. Dilworth, M. Girardi and J. Hagler, Dual Banach spaces which contain an isometric copy of , Bull. Polon. Acad. Sci. 48 (2000), 112. MR 2001e:46016
 [DJLT]
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), 167174. MR 97d:46010
 [DL]
P. N. Dowling and C. J. Lennard, Every nonreflexive subspace of fails the fixed point property, Proc. Amer. Math. Soc. 125 (1997), 443446. MR 97d:46034
 [DLT]
P. N. Dowling, C. J. Lennard and B. Turett, Reflexivity and the fixedpoint property for neonexpansive maps, J. Math. Analysis and Applications 200 (1996), 653662. MR 97c:47062
 [DRT]
Patrick N. Dowling, Narcisse Randrianantoanina and Barry Turett, Remarks on James's distortion theorems, Bull. Austral. Math. Soc. 57 (1998), 4954. MR 99b:46014
 [H1]
J. Hagler, Embeddings of into conjugate Banach spaces, Ph.D. Thesis, University of California, Berkeley, Calif., 1972.
 [H2]
J. Hagler, Some more Banach spaces which contain , Studia Math. 46 (1973), 3542. MR 48:11995
 [HS]
J. Hagler and C. Stegall, Banach spaces whose duals contain complemented subspaces isomorphic to , J. Funct. Anal.13 (1973), 233251. MR 50:2874
 [J]
W. B. Johnson, A complementably universal conjugate Banach space and its relation to the approximation property,Israel J. Math. 13 (1972), 301310. MR 48:4700
 [JRZ]
W. B. Johnson, H. P. Rosenthal and M. Zippin, On bases, finite dimensional decompositions and weaker structures in Banach spaces, Israel J. Math. 9 (1971), 488506. MR 43:6702
 [L]
J. Lindenstrauss, A short proof of Liapounoff's convexity theorem, J. Math. and Mech. 15 (1966), 971972. MR 34:7754
 [LR]
J. Lindenstrauss and H. P. Rosenthal, The spaces, Israel J. Math. 7 (1969), 325349. MR 42:5012
 [P]
A. Peczynski, On Banach spaces containing , Studia Math. 30 (1968), 231246. MR 38:521
 [R]
H. P. Rosenthal, On factors of with nonseparable dual, Israel J. Math. 13 (1972), 361378. MR 52:8900
 [S]
C. Stegall, Banach spaces whose duals contain with applications to the study of dual spaces, Trans. Amer. Math. Soc. 176 (1993), 463477. MR 47:3953
 [DGH]
 S. Dilworth, M. Girardi and J. Hagler, Dual Banach spaces which contain an isometric copy of , Bull. Polon. Acad. Sci. 48 (2000), 112. MR 2001e:46016
 [DJLT]
 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), 167174. MR 97d:46010
 [DL]
 P. N. Dowling and C. J. Lennard, Every nonreflexive subspace of fails the fixed point property, Proc. Amer. Math. Soc. 125 (1997), 443446. MR 97d:46034
 [DLT]
 P. N. Dowling, C. J. Lennard and B. Turett, Reflexivity and the fixedpoint property for neonexpansive maps, J. Math. Analysis and Applications 200 (1996), 653662. MR 97c:47062
 [DRT]
 Patrick N. Dowling, Narcisse Randrianantoanina and Barry Turett, Remarks on James's distortion theorems, Bull. Austral. Math. Soc. 57 (1998), 4954. MR 99b:46014
 [H1]
 J. Hagler, Embeddings of into conjugate Banach spaces, Ph.D. Thesis, University of California, Berkeley, Calif., 1972.
 [H2]
 J. Hagler, Some more Banach spaces which contain , Studia Math. 46 (1973), 3542. MR 48:11995
 [HS]
 J. Hagler and C. Stegall, Banach spaces whose duals contain complemented subspaces isomorphic to , J. Funct. Anal.13 (1973), 233251. MR 50:2874
 [J]
 W. B. Johnson, A complementably universal conjugate Banach space and its relation to the approximation property,Israel J. Math. 13 (1972), 301310. MR 48:4700
 [JRZ]
 W. B. Johnson, H. P. Rosenthal and M. Zippin, On bases, finite dimensional decompositions and weaker structures in Banach spaces, Israel J. Math. 9 (1971), 488506. MR 43:6702
 [L]
 J. Lindenstrauss, A short proof of Liapounoff's convexity theorem, J. Math. and Mech. 15 (1966), 971972. MR 34:7754
 [LR]
 J. Lindenstrauss and H. P. Rosenthal, The spaces, Israel J. Math. 7 (1969), 325349. MR 42:5012
 [P]
 A. Peczynski, On Banach spaces containing , Studia Math. 30 (1968), 231246. MR 38:521
 [R]
 H. P. Rosenthal, On factors of with nonseparable dual, Israel J. Math. 13 (1972), 361378. MR 52:8900
 [S]
 C. Stegall, Banach spaces whose duals contain with applications to the study of dual spaces, Trans. Amer. Math. Soc. 176 (1993), 463477. MR 47:3953
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Additional Information
J. Hagler
Affiliation:
Department of Mathematics, University of Denver, Denver, Colorado 80208
Email:
jhagler@math.du.edu
DOI:
http://dx.doi.org/10.1090/S0002993902064742
PII:
S 00029939(02)064742
Keywords:
Banach spaces,
complemented isometric copies of $L_1$,
$\left( 1,K\right) $\emph{}asymptotic copies of\emph{ }$\left( \ell_{1}\oplus\sum_{n}\ell_{\infty}^{n}\right) _{1}$
Received by editor(s):
January 30, 2001
Received by editor(s) in revised form:
June 13, 2001
Published electronically:
March 25, 2002
Additional Notes:
The author would especially like to thank H. P. Rosenthal and C. Stegall. Thanks also go to M. Girardi, S. Dilworth, W. B. Johnson and the referee for helpful comments and suggestions
Communicated by:
N. TomczakJaegermann
Article copyright:
© Copyright 2002 American Mathematical Society
