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1answer
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Element $a$ of a C*-algebra such that $f(a^*a) = 0$ but $f(aa^*) \neq 0$ for some positive linear functional $f$

Could somebody please give me an example, assuming one exists, of an element $a$ of a C*-algebra $A$ such that $f(a^*a) = 0$ but $f(aa^*) \neq 0$ for some positive linear functional $f:A \to ...
1
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2answers
152 views

If a sub-C*-algebra does not contain the unit, is it contained in a proper ideal?

Suppose that $R$ and $S$ are unital rings and that $S$ is a subring of $R$ in the weak sense where the multiplicative identities $1_R$ and $1_S$ are not assumed to be the same. In fact, assume $1_R ...