Corrigendum to: ``Bishop's property \((\beta)\) for paranormal operators'' and ``SVEP and Bishop's property \(( \beta )\) for \(k\ast\)-paranormal operators'' (Q2869941)
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scientific article; zbMATH DE number 6243264
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Corrigendum to: ``Bishop's property \((\beta)\) for paranormal operators'' and ``SVEP and Bishop's property \(( \beta )\) for \(k\ast\)-paranormal operators'' |
scientific article; zbMATH DE number 6243264 |
Statements
7 January 2014
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quasi-paranormal operator
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\(k\ast\)-paranormal operator
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property (II)
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Bishop's property \((\beta)\)
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SVEP
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0.8972927
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0.8703077
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0.86734766
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0.86421764
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0.8583718
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0.8576552
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0.8505773
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Corrigendum to: ``Bishop's property \((\beta)\) for paranormal operators'' and ``SVEP and Bishop's property \(( \beta )\) for \(k\ast\)-paranormal operators'' (English)
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The authors have discovered a fatal gap in the proof of Theorem 3.5, claiming that ``if an operator \(T\) has the property (II), then \(T\) also has Bishop's property (\(\beta\))'' in [\textit{A. Uchiyama} and \textit{K. Tanahashi}, Oper. Matrices 3, No.~4, 517--524 (2009; Zbl 1198.47039)], and they provide a counterexample. This also necessitates a reformulation of Theorem~1 of [\textit{N. L. Braha} and \textit{K. Tanahashi}, Oper. Matrices 5, No.~3, 469--472 (2011; Zbl 1237.47022)].
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