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Dual complementors on Banach algebras


Author: B. J. Tomiuk
Journal: Proc. Amer. Math. Soc. 103 (1988), 815-822
MSC: Primary 46H20; Secondary 46K05
DOI: https://doi.org/10.1090/S0002-9939-1988-0947665-8
MathSciNet review: 947665
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Abstract: We study semisimple annihilator Banach algebras $ A$ with a right complementor $ p$ such that the mapping $ q$ on the closed left ideals $ J$ of $ A$ given by $ {J^q} = {l_A}({[{r_A}(J)]^p})$ is a left complementor on $ A$. A right complementor $ p$ with this property is called dual, and the pair $ (p,q)$ is called a dual pair of complementors on $ A$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0947665-8
Keywords: Right complemented Banach algebra, dual right complementor, dual Banach algebra, $ {A^ * }$-algebra, $ {B^ * }$-algebra
Article copyright: © Copyright 1988 American Mathematical Society

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