On Some Normality-Like Properties and Bishop's Property (𝛽) for a Class of Operators on Hilbert Spaces
We prove some further properties of the operator 𝑇∈[𝑛QN] (𝑛-power quasinormal, defined in Sid Ahmed, 2011). In particular we show that the operator 𝑇∈[𝑛QN] satisfying the translation invariant property is normal and that the operator 𝑇∈[𝑛QN] is not supercyclic provided that it is not invertible. Als...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/975745 |
| Summary: | We prove some further properties of the operator 𝑇∈[𝑛QN]
(𝑛-power quasinormal, defined in Sid Ahmed, 2011). In particular we show that the operator
𝑇∈[𝑛QN] satisfying the translation invariant property is normal and that the
operator 𝑇∈[𝑛QN] is not supercyclic provided that it is not invertible. Also, we
study some cases in which an operator 𝑇∈[2QN] is subscalar of order 𝑚; that is, it is
similar to the restriction of a scalar operator of order 𝑚 to an invariant subspace. |
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| ISSN: | 0161-1712 1687-0425 |