Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Banach spaces failing the almost isometric universal extension property

Author(s): D. M. Speegle
Journal: Proc. Amer. Math. Soc. 126 (1998), 3633-3637.
MSC (1991): Primary 46B20
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: If $X$ is an infinite dimensional, separable, uniformly smooth Banach space, then there is an $\epsilon > 0$, a Banach space $Y$ containing $X$ as a closed subspace and a norm one map $T$ from $X$ to a $C(K)$ space which does not extend to an operator $\tilde T$ from $Y$ to $C(K)$ with $\|\tilde T\| \le 1+\epsilon $.

References:

[J]
W. B. Johnson, Extensions of $c_{0}$, Positivity (to appear).

[JZ]
W. B. Johnson and M. Zippin, Extensions of operators from subspaces of $c_{0}(\gamma )$ into $C(K)$ spaces, Proc. AMS 107 (1989), 751-754. MR 90b:46045

[K]
J. A. Kalman, Continuity and convexity of projections and barycentric coordinates in convex polyhedra, Pacific J. Math 22 (1961), 1017-1022. MR 24:A3557

[L]
J. Lindenstrauss, Extension of compact operators, Memoirs of the AMS 48 (1964). MR 31:3828

[LP]
J. Lindenstrauss and A. Pelczynski, Contributions to the theory of classical Banach spaces, J. Functional Analysis 8 (1971), 225-249. MR 45:863

[R]
H. L. Royden, Real Analysis 3rd Ed., Macmillan, New York, 1988. MR 90g:00004

[S]
A. Sobczyk, Projection of the space $m$ on its subspace $c_{0}$, Bull. Amer. Math. Soc. 47 (1941), 938-947. MR 3:205f

[Z]
M. Zippin, A global approach to certain operator extension problems, Lecture Notes in Math. 1470 (1991), 78-94. MR 93b:47011

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46B20

Retrieve articles in all Journals with MSC (1991): 46B20

Additional Information:

D. M. Speegle
Affiliation: Department of Mathematics, Texas A~&~M University, College Station, Texas 77843
Address at time of publication: Department of Mathematics, Saint Louis University, Saint Louis, Missouri 63103
Email: speegle@math.tamu.edu

DOI: 10.1090/S0002-9939-98-04517-1
PII: S 0002-9939(98)04517-1
Received by editor(s): December 23, 1996
Received by editor(s) in revised form: April 25, 1997
Additional Notes: The author was supported in part by the NSF through the Workshop in Linear Analysis and Probability at Texas A&M
Communicated by: Dale Alspach
Copyright of article: Copyright 1998, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google