Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-25T05:07:43.075Z Has data issue: false hasContentIssue false
  • English
  • Français

On some Banach space sequences

Published online by Cambridge University Press:  17 April 2009

Roshdi Khalil
Roshdi Khalil
Affiliation:
Department of Mathematics, University of Kuwait, PO Box 5969, Kuwait.
Rights & Permissions [Opens in a new window]

Abstract

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.

We introduce the Banach space of vector valued sequences lp, q(E), 1 ≤ p, q ≤ ∞, where E is a Banach space. Then we study the relation between lp, q(E) and the Schur multipliers of lpE, where E is taken to be some lr.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 25 , Issue 2 , April 1982 , pp. 231 - 241
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Apiola, Heikki, “Duality between spaces of p-summable sequences, (p, q)-summing operators and characterizations of nuclearity”, Math. Ann. 219 (1976), 53–64.Google Scholar
[2]Bennett, G., “Schur multipliers”, Duke Math. J. 44 (1977), 603–139.CrossRefGoogle Scholar
[3]Cohen, Joel S., “Absolutely P-summing, P-nuclear operators and their conjugates”, Math. Ann. 201 (1973), 177–200.CrossRefGoogle Scholar
[4]Diestel, J. and Uhl, J.J. Jr, Vector measures (Mathematical Surveys, 15. American Mathematical Society, Providence, Rhode Island, 1977).Google Scholar
[5]Grothendieck, A., “Sur certaines classes de suites dans les espaces de Banach et le théorèm de Dvoretzky-Rogers”, Bol. Soc. Mat. São Paulo 8 (1953), 81–110 (1956).Google Scholar
[6]Khalil, Roshdi, “Trace-class norm multipliers”, Proc. Amer. Math. Soc. 79 (1980), 379–387.CrossRefGoogle Scholar
[7]Khalil, Roshdi, “On the algebra of multipliers”, Canad. J. Math. (to appear).Google Scholar
[8]Khalil, Roshdi, “Pointwise multipliers”, J. Univ. Kuwait Sci. (to appear).Google Scholar
[9]Köthe, Gottfried, Topologioal vector spaces. I (translated by Garling, D.J.H.. Die Grundlehren der mathematischen Wissenschaften, 159. Springer-Verlag, Berlin, Heidelberg, New York, 1969).Google Scholar
[10]Lindenstrauss, J. and Pełczynski, A., “Absolutely summing operators in Lp-spaces and their applications”, Studia Math. 29 (1968), 275–326.CrossRefGoogle Scholar
[11]Pietsch, Albrecht, Theorie der Operatorenideale (Zusammenfassung) (Wissenschaftliche Beiträge der Friedrich-Schiller-Universität Jena. Friedrich-Schiller-Universität, Jena, 1972).Google Scholar
[12]Royden, H.L., Real analysis (MaCmillan, New York; Collier-Macmillan, London; 1963).Google Scholar