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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Continuity and linearity of centralizers on a complemented algebra.

Authors: Parfeny P. Saworotnow and George R. Giellis
Journal: Proc. Amer. Math. Soc. 31 (1972), 142-146
MathSciNet review: 0288585
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Abstract: Let $ A$ be a semisimple complemented algebra and let $ T$ be a mapping of $ A$ into itself such that either $ T(xy) = xTy$ or $ T(xy) = (Tx)y$ holds for all $ x,y \in A$. If $ T$ is defined everywhere on $ A$ then $ T$ is a bounded linear operator.

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Keywords: Centralizer, right centralizer, left centralizer, complemented algebra, $ {H^\ast}$-algebra, right $ {H^\ast}$-algebra, left $ {H^\ast}$-algebra, left projection, primitive left projection
Article copyright: © Copyright 1972 American Mathematical Society