Continuity and linearity of centralizers on a complemented algebra.

Saworotnow, Parfeny P.; Giellis, George R.

doi:10.1090/S0002-9939-1972-0288585-2

Continuity and linearity of centralizers on a complemented algebra.
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by Parfeny P. Saworotnow and George R. Giellis

Proc. Amer. Math. Soc. 31 (1972), 142-146

DOI: https://doi.org/10.1090/S0002-9939-1972-0288585-2

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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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Bibliographic Information

Journal: Proc. Amer. Math. Soc. 31 (1972), 142-146
DOI: https://doi.org/10.1090/S0002-9939-1972-0288585-2
MathSciNet review: 0288585