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Complemented Banach Algebras

Published online by Cambridge University Press:  20 November 2018

A. Olubummo
A. Olubummo*
Affiliation:
University of Ibadan, Ibadan, Nigeria
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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

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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