On p-quasi-hyponormal operators

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• 作者：B.P. Duggal ; In Ho Jeon
• 关键词：p-quasi-hyponormal operator ; Supercyclic ; Continuity of the spectrum ; Weyl’ ; s theorem
• 刊名：Linear Algebra and its Applications
• 出版年：2007
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：1 April 2007
• 卷：422
• 期：1
• 页码：331-340
• 文件大小：167 K

摘要

A Hilbert space operator A B(H) is said to be p-quasi-hyponormal for some 0 < p 1, A p − QH, if A^*(A^2p − A^*2p)A 0. If H is infinite dimensional, then operators A p − QH are not supercyclic. Restricting ourselves to those A p − QH for which A⁻¹(0) A^*-1(0), A p_* − QH, a necessary and sufficient condition for the adjoint of a pure p_* − QH operator to be supercyclic is proved. Operators in p_* − QH satisfy Bishop’s property (β). Each A p_* − QH has the finite ascent property and the quasi-nilpotent part H₀(A − λI) of A equals (A − λI)^-1(0) for all complex numbers λ; hence f(A) satisfies Weyl’s theorem, and f(A^*) satisfies a-Weyl’s theorem, for all non-constant functions f which are analytic on a neighborhood of σ(A). It is proved that a Putnam–Fuglede type commutativity theorem holds for operators in p_* − QH.