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Example of a ternary Lie ideal which is not a Lie ideal

Let $H$ and $K$ be Hilbert spaces and $V\subset B(H,K)$ be a ternary ring of operators i.e. $xy^*z \in V$ for all $x,y,z \in V$. Let $I$ be a closed subspace of $V$. $I$ is called a ternary Lie ideal ...
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A locally convex $C^*$ algebra without zero divisor

Let we have a locally convex $C^*$ algebra $A$. That is $A$ is a TVS equipped with an algebra and an involution structure such that all operations are continuous. Moreover the topology on $A$ ...
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