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- Title
ON OPERATORS SATISFYING T*(T*²T²)<sup>p</sup>T ≥ T*(T²T*²)<sup>p</sup>T.
- Authors
FEI ZUO; MECHERI, SALAH
- Abstract
An operator T ∈ B(H) is called square-p -quasihyponormal if T*(T*²T²)pT ≥ T*(T²T*²)pT for p ∈ (0,1], which is a further generalization of normal operator. In this paper, we give a sufficient condition for an injective square-p-quasihyponormal operator to be self-adjoint, and we obtain that every square-p-quasihyponormal operator has a scalar extension. As a consequence, we prove that if T is a quasiaffine transform of square-p -quasihyponormal, then T satisfies Weyl's theorem. Finally some examples are presented.
- Subjects
OPERATOR theory; MATRICES (Mathematics); HYPONORMAL operators; WEYL theory of boundary value problems; LINEAR operators; HILBERT space
- Publication
Operators & Matrices, 2022, Vol 16, Issue 3, p645
- ISSN
1846-3886
- Publication type
Article
- DOI
10.7153/oam-2022-16-47