1. METRIC VERSIONS OF POSNER’S THEOREMS
- Author
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J. Alaminos, J. Extremera, Špela Špenko, Armando R. Villena, Mathematics, and Algebra
- Subjects
Analyse fonctionnelle ,Mathematics(all) ,General Mathematics ,46H05 ,Ultraprime banach algebra ,Linear operators ,Zero (complex analysis) ,derivation ,Algèbre - théorie des anneaux - théorie des corps ,Combinatorics ,Identity (mathematics) ,Banach algebra ,Metric (mathematics) ,47B47 ,Commutative property ,47B48 ,Centralizing map ,Mathematics - 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.
- Published
- 2012