Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Covering a compact set in a Banach space by an operator range of a Banach space with basis


Authors: V. P. Fonf, W. B. Johnson, A. M. Plichko and V. V. Shevchyk
Journal: Trans. Amer. Math. Soc. 358 (2006), 1421-1434
MSC (2000): Primary 46B28; Secondary 46B15, 46B25, 46B50
Published electronically: September 9, 2005
MathSciNet review: 2186980
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A Banach space $X$ has the approximation property if and only if every compact set in $X$ is in the range of a one-to-one bounded linear operator from a space that has a Schauder basis. Characterizations are given for $\mathcal{L}_p$spaces and quotients of $\mathcal{L}_p$ spaces in terms of covering compact sets in $X$ by operator ranges from $\mathcal{L}_p$ spaces. A Banach space $X$is a $\mathcal{L}_1$ space if and only if every compact set in $X$ is contained in the closed convex symmetric hull of a basic sequence which converges to zero.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 46B28, 46B15, 46B25, 46B50

Retrieve articles in all journals with MSC (2000): 46B28, 46B15, 46B25, 46B50


Additional Information

V. P. Fonf
Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel — and — Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: fonf@black.bgu.ac.il

W. B. Johnson
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: johnson@math.tamu.edu

A. M. Plichko
Affiliation: Instytut Matematyki, Politechnika Krakowska im. Tadeusza Kosciuszki, ul. Warszawska 24, Krakow 31-155, Poland
Email: aplichko@usk.pk.edu.pl

V. V. Shevchyk
Affiliation: Sebastian-Kneipp Gasse, 7, Augsburg 86152, Germany
Email: vshevchyk@hotmail.com

DOI: http://dx.doi.org/10.1090/S0002-9947-05-04083-3
PII: S 0002-9947(05)04083-3
Received by editor(s): September 7, 2001
Received by editor(s) in revised form: July 9, 2002
Published electronically: September 9, 2005
Additional Notes: The second author was supported in part by NSF DMS-9900185, DMS-0200690, Texas Advanced Research Program 010366-0033-20013, and the U.S.-Israel Binational Science Foundation
The third author was supported in part by the DAAD Foundation
Article copyright: © Copyright 2005 by the authors