Abstract
Let $S$ and $T$ be continuous linear operators on an ultraprime Banach algebra $A$. We show that if $S$, $T$, and $ST$ are close to satisfy the derivation identity on $A$, then either $S$ or $T$ approaches to zero. If $T$ is close to satisfy the derivation identity and $[T(a),a]$ is near the centre of $A$ for each $a \in A$, then either $T$ approaches to zero or $A$ is nearly commutative. Further, we give quantitative estimates of these phenomena.
Citation
J. Alaminos. J. Extremera. Š. Špenko. A. R. Villena. "METRIC VERSIONS OF POSNER’S THEOREMS." Taiwanese J. Math. 16 (6) 1951 - 1957, 2012. https://doi.org/10.11650/twjm/1500406832
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