Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-26T23:40:30.752Z Has data issue: false hasContentIssue false
  • English
  • Français

A representation theorem for partially ordered Banach algebras

Published online by Cambridge University Press:  24 October 2008

Kung-Fu Ng
Kung-Fu Ng
Affiliation:
University College, Swansea
Get access Rights & Permissions [Opens in a new window]

Extract

Let be a real algebra which is also a Banach space. Then is called a partially ordered Banach algebra if there is specified a non-empty subset of , called the positive cone, such that

and

(A 5) is 1-normal and closed. (We recall that is said to be 1-normal if

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 1 , January 1968 , pp. 53 - 59
Copyright
Copyright © Cambridge Philosophical Society 1968

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Kadison, R. V.A representation theory for commutative topological algebras. Mem. Amer. Math. Soc. 7 (1951).Google Scholar
(2)Grosberg, J. and Krein, M.Sur la décomposition des functionnelles on composantes positives. Dokl. Akad. Nauk SSSR (N.S.), 25 (1939), 723–726.Google Scholar
(3)Simmons, G. F.Introduction to topology and modern analysis (McGraw-Hill, 1963).Google Scholar