Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-28T15:40:16.820Z Has data issue: false hasContentIssue false
  • English
  • Français

Unbounded approximate identities in normed algebras

Published online by Cambridge University Press:  18 May 2009

P. G. Dixon
P. G. Dixon
Affiliation:
Dept. of Pure Mathematics, University of Sheffield, Sheffield, S3 7RH, England.
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.

The object of this paper is to consider two easy propositions concerning bounded approximate identities and show that they do not extend to unbounded approximate identities. The propositions are as follows.

Proposition 1.1. Every bounded left approximate identity in a normed algebra is a left approximate identity for the completion.

Proposition 1.2. Every bounded left approximate identity in a separable normed algebra has a subsequence which is a left approximate identity.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 2 , May 1992 , pp. 189 - 192
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

REFERENCES

1.Dixon, P. G., Approximate identities in normed algebras II, J. London Math. Soc. (2), 17 (1978), 141–151.Google Scholar
2.Dixon, P. G., Factorization and unbounded approximate identities in Banach algebras, Math. Proc. Camb. Philos. Soc., 107 (1990), 557–571.Google Scholar
3.Doran, R. S. and Wichmann, J., Approximate identities and factorization in Banach modules. Lecture Notes in Mathematics 768, (Springer, 1979).Google Scholar
4.Willis, G., Examples of factorization without bounded approximate units, Proc. London Math. Soc. to appear.Google Scholar