Lie and Jordan Ideals in Reflexive Algebras |
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Authors: | Fangyan Lu Xiuping Yu |
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Institution: | (1) Department of Mathematics, Suzhou University, Suzhou, 215006, P. R. China |
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Abstract: | A CDCSL algebra is a reflexive operator algebra with completely distributive and commutative subspace lattice. In this paper,
we show, for a weakly closed linear subspace
of a CDCSL algebra
, that
is a Lie ideal if and only if
for all invertibles A in
, and that
is a Jordan ideal if and only if it is an associative ideal. |
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Keywords: | 47L35 47L35 17B30 17C65 |
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