Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-16T21:17:13.378Z Has data issue: false hasContentIssue false
  • English
  • Français

Semi-embeddings of Banach spaces which are hereditarily c0

Published online by Cambridge University Press:  20 January 2009

L. Drewnowski
L. Drewnowski
Affiliation:
Institute of Mathematics, A. Mickiewicz University, Poznaṅ, Poland
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Following Lotz, Peck and Porta [9], a continuous linear operator from one Banach space into another is called a semi-embedding if it is one-to-one and maps the closed unit ball of the domain onto a closed (hence complete) set. (Below we shall allow the codomain to be an F-space, i.e., a complete metrisable topological vector space.) One of the main results established in [9] is that if X is a compact scattered space, then every semi-embedding of C(X) into another Banach space is an isomorphism ([9], Main Theorem, (a)⇒(b)).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 26 , Issue 2 , June 1983 , pp. 163 - 167
Copyright
Copyright © Edinburgh Mathematical Society 1983

References

REFERENCES

1.Diestel, J. and Uhl, J. J. Jr. Vector Measures (American Mathematical Society, Mathematical surveys, number 15, 1977).CrossRefGoogle Scholar
2.Drewnowski, L., On minimally subspace-comparable F-spaces, J. Fund. Analysis 26 (1977), 315–332.CrossRefGoogle Scholar
3.Drewnowski, L., An extension of a theorem of Rosenthal on operators acting from l∞(Γ), Studia Math. 57 (1976), 209–215.CrossRefGoogle Scholar
4.Drewnowski, L., Un théorème sur les opérateurs de l∞(Γ), C. R. Acad. Sci. Paris, Sér. A, 281 (1975), 967–969.Google Scholar
5.Hagler, J., A counterexample to several questions about -Banach spaces, Studia Math. 60 (1977), 289–308.Google Scholar
6.Kalton, N. J., Basic sequences in F-spaces and their applications, Proc. Edinburgh Math. Soc. 19 (1974), 151–167.CrossRefGoogle Scholar
7.Lindenstrauss, J. and Tzafriri, L., Classical Banach Spaces I. Sequence Spaces (Ergebnisse derMath. 92, Springer, Berlin-Heidelberg-New York, 1977).Google Scholar
8.Lindenstrauss, J. and Tzafriri, L., Classical Banach Spaces II. Function Spaces (Ergebnisse derMath. 97, Springer, Berlin-Heidelberg-New York, 1979).CrossRefGoogle Scholar
9.Lotz, H. P., Peck, N. T. and Porta, H., Semi-embeddings of Banach spaces, Proc. Edinburgh Math. Soc. 22 (1979), 233–240.CrossRefGoogle Scholar
10.Petczyñski, A. and Semadeni, Z., Spaces of continuous functions (III), Studia Math. 18 (1959), 211–222.CrossRefGoogle Scholar
11.Rosenthal, H. P., On relatively disjoint families of measures, with some applications toBanach space theory, Studia Math. 37 (1970), 13–36.CrossRefGoogle Scholar