Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-02-03T17:14:55.905Z Has data issue: false hasContentIssue false
  • English
  • Français

A decomposition property of weak Lî

Published online by Cambridge University Press:  20 January 2009

N. T. Peck
N. T. Peck
Affiliation:
University of IllinoisDepartment of Mathematics1409 West Green StreetUrbana, Illinois 61801, USA
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.

Let be a set of disjointly supported, positive functions in the Banach envelope of weak L1. We prove that each fi can be written as ei + gi where ei and gi, are disjointly supported and satisfy these additional properties: the ei's are isometrically the basis in the envelope norm; the envelope norm of a linear combination of the gi's is equal to the envelope norm of the corresponding combination of the fi's.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 1 , February 1992 , pp. 109 - 114
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

REFERENCES

1.Cwikel, M. and Fefferman, C., Maximal seminorms on weak L 1, Studio Math. 69 (1980), 149–154.CrossRefGoogle Scholar
2.Lotz, H. P. and Peck, N. T., On Banach sublattices of weak L 1, Proc. Amer. Math. Soc., to appear.Google Scholar
3.Peck, N. T. and Talagrand, M., Banach sublattices of Weak L 1, Israel J. Math. 59 (1987), 257–271.Google Scholar