METRIC VERSIONS OF POSNER'S THEOREMS

LetSandTbe continuous linear operators on an ultraprime Banach algebraA. We show that ifS,T, andSTare close to satisfy the derivation identity onA, then eitherSorTapproaches to zero. IfTis close to satisfy the derivation identity and [T(a),a] is near the centre ofAfor eacha∈A, then eitherTapproaches...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 15; no. 6; pp. 1951 - 1957
Main Authors Alaminos, J., Extremera, J., Špenko, Š., Villena, A. R.
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.12.2012
Subjects
Algebra
Mathematical theorems
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Summary:LetSandTbe continuous linear operators on an ultraprime Banach algebraA. We show that ifS,T, andSTare close to satisfy the derivation identity onA, then eitherSorTapproaches to zero. IfTis close to satisfy the derivation identity and [T(a),a] is near the centre ofAfor eacha∈A, then eitherTapproaches to zero orAis nearly commutative. Further, we give quantitative estimates of these phenomena. 2010Mathematics Subject Classification: Primary 46H05; Secondary 47B47, 47B48. Key words and phrases: Derivation, Ultraprime Banach algebra, Centralizing map.
ISSN:1027-5487
2224-6851