Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-15T10:17:34.733Z Has data issue: false hasContentIssue false
  • English
  • Français

Convolution operators associated with vector measures

Published online by Cambridge University Press:  18 May 2009

Mangatiana A. Robdera  and
Paulette Saab
Mangatiana A. Robdera
Affiliation:
Mangatiana A. Robdera William Paterson College, 300 Pompto N Rd.Wayne, NJ 07470, E-mail: robdera@frontier.wilpaterson.edu
Paulette Saab
Affiliation:
Paulette Saab Department of Mathematics, University of Missouri, Columbia, Mo 65211, E-mail: paula@math.missouri.edu
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.

Inthis note, we present a thorough investigation of convolution operators that are naturally associated to vector measures. We characterize those convolution operators that are weakly compact and compact on Ll(G) and C(G) as well as those that are p summing, (1 ≤ p ≤ ∞) and nuclear on C(G).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 40 , Issue 3 , September 1998 , pp. 367 - 384
Copyright
Copyright © Glasgow Mathematical Journal Trust 1998

References

REFERENCES

1.Bukhvalov, A. V. and Danielevich, A. A., Boundary properties of analytic and harmonic functions with values in Banach space, Mat. Zametki, 31, (1982), 203–214.Google Scholar
2.Dinculeanu, N., Vector measures (Pergamon Press, 1967).CrossRefGoogle Scholar
3.Diestel, J., Jarchow, H. and Tonge, A., Absolutely summing operators, Cambridge studies in advanced mathematics 43 (Cambridge University Press, 1995).CrossRefGoogle Scholar
4.Diestel, J. and Uhl, J. J. Jr, Vector measures, Math. Surveys, 15 (AMS, Providence, RI, 1977).Google Scholar
5.Girardi, M. K., Ph.D. Thesis (University of Illinois, 1990).Google Scholar
6.Hewitt, E. and Ross, K. A., Abstract harmonic analysis I-II (Springer-Verlag, 1970).Google Scholar
7.Katznelson, Y., An introduction to harmonic analysis (Dover Publication Inc, New York, 1976).Google Scholar
8.Lust-Piquard, F., Properties geometriques des sous-espaces invariants par translation de L1(G) et C(G), Seminaire sur la geometrie des espaces de Banach, Ecole Polytechnique, 26, (1977–1978).Google Scholar
9.Musial, K., Martingales of Pettis integrable functions, in Measure theory, Oberwolfach, 1979. Lecture Notes in Mathematics 794, (Springer-Verlag, 1980).Google Scholar
10.Singer, I., Sur la meilleure approximation des fonctions abstraites continues a valeurs dans un espace de Banach, Rev. Roumaine Math. Pures Appl., 2, (1957), 245–262.Google Scholar
11.Wojtaszczyk, P., Banach spaces for analysts (Cambridge University Press, 1991).CrossRefGoogle Scholar