We show that the commutativity, the associativity and the distributivity of the operation $a\circ b=\sqrt{a}b\sqrt{a}$ on the set of all positive invertible elements of a C*-algebra $\mathcal{A}$ are all equivalent to the commutativity of $\mathcal{A}$. We also present abstract characterizations of the operation $\circ$ and a few related ones too.
On the standard K-loop structure of positive invertible elements in a C*-algebra,
BENEDUCI, Roberto;
2014-01-01
Abstract
We show that the commutativity, the associativity and the distributivity of the operation $a\circ b=\sqrt{a}b\sqrt{a}$ on the set of all positive invertible elements of a C*-algebra $\mathcal{A}$ are all equivalent to the commutativity of $\mathcal{A}$. We also present abstract characterizations of the operation $\circ$ and a few related ones too.File in questo prodotto:
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