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On Some Normality-Like Properties and Bishop's Property ( ð ›½ ) for a Class of Operators on Hilbert Spaces

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  • Sid Ahmed Ould Ahmed Mahmoud

Abstract

We prove some further properties of the operator 𠑇 ∈ [ 𠑛 Q N ] ( 𠑛 -power quasinormal, defined in Sid Ahmed, 2011). In particular we show that the operator 𠑇 ∈ [ 𠑛 Q N ] satisfying the translation invariant property is normal and that the operator 𠑇 ∈ [ 𠑛 Q N ] is not supercyclic provided that it is not invertible. Also, we study some cases in which an operator 𠑇 ∈ [ 2 Q N ] is subscalar of order 𠑚 ; that is, it is similar to the restriction of a scalar operator of order 𠑚 to an invariant subspace.

Suggested Citation

  • Sid Ahmed Ould Ahmed Mahmoud, 2012. "On Some Normality-Like Properties and Bishop's Property ( ð ›½ ) for a Class of Operators on Hilbert Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-20, June.
    • Handle: RePEc:hin:jijmms:975745
    DOI: 10.1155/2012/975745
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