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标题：On Some Normality-Like Properties and Bishop's Property (<svg style="vertical-align:-3.294pt;width:12.6375px;" id="M1" height="19.200001" version="1.1" viewBox="0 0 12.6375 19.200001" width="12.6375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.2)"> <g transform="translate(72,-56.64)"> <text transform="matrix(1,0,0,-1,-71.95,59.97)"> <tspan style="font-size: 17.93px; " x="0" y="0">𝛽</tspan> </text> </g> </g> </svg>) for a Class of Operators on Hilbert Spaces
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作者：Sid Ahmed Ould Ahmed Mahmoud
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2012
卷号：2012
DOI：10.1155/2012/975745
出版社：Hindawi Publishing Corporation
摘要：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.