Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-15T05:45:05.965Z Has data issue: false hasContentIssue false
  • English
  • Français

Complemented Banach Algebras

Published online by Cambridge University Press:  20 November 2018

A. Olubummo
A. Olubummo*
Affiliation:
University of Ibadan, Ibadan, Nigeria
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 A be a complex Banach algebra and Lr (Ll) be the lattice of all closed right (left) ideals in A. Following Tomiuk (5), we say that A is a right complemented algebra if there exists a mapping I —> IP of Lτ into Lr such that if I ∊ Lr, then I ∩ Ip = (0), (Ip)p = I, I ⴲ Ip = A and if I1, I2 ∊ Lr with I1 ⊆ I2 then .

If in a Banach algebra A every proper closed right ideal has a non-zero left annihilator, then A is called a left annihilator algebra. If, in addition, the corresponding statement holds for every proper closed left ideal and r(A) = (0) = l(A), A is called an annihilator algebra (1).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 149 - 150
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Bonsall, F. F. and Goldie, A. W., Annihilator algebras, Proc. London Math. Soc. (3), 4 (1954), 154–167.Google Scholar
2. Bonsall, F. F., A minimal property of the norm in some Banach algebras, J. London Math. Soc, 29 (1954), 157–163.Google Scholar
3. Kaplansky, I., Normed algebras, Duke Math. J., 16 (1949), 399–418.Google Scholar
4. Olubummo, A., Weakly compact Bf-algebras, To appear in Proc. Amer. Math. Soc.Google Scholar
5. Tomiuk, B. J., Structure theory of complemented Banach algebras, Can. J. Math., 14 (1962), 651–659.Google Scholar