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- W2339992334 abstract "An operator $Ain B(mathcal{H})$ , the algebra of bounded linear transformations on a complex infinite dimensional Hilbert space $mathcal{H}$ , belongs to class $mathcal{A}(n)$ (resp., $mathcal{A}(*-n)$ ) if $vert Avert^{2}leqvert A^{n+1}vert^{frac{2}{n+1}}$ (resp., $vert A^{*}vert^{2}leq vert A^{n+1}vert^{frac{2}{n+1}}$ ) for some integer $ngeq1$ , and an operator $Ain B(mathcal{H})$ is called n-paranormal, denoted $Ain mathcal{P}(n)$ (resp., $*-n$ -paranormal, denoted $Ain mathcal{P}(*-n)$ ) if $Vert AxVert ^{n+1}leq Vert A^{n+1}xVert Vert xVert ^{n}$ (resp., $Vert A^{*}xVert ^{n+1}leq Vert A^{n+1}xVert Vert xVert ^{n}$ ) for some integer $ngeq 1$ and all $x inmathcal{H}$ . In this paper, we prove that if $Ain{mathcal{A}(n)cup mathcal{P}(n)}$ (resp., $Ain{mathcal{A}(*-n)cup mathcal{P}(*-n)}$ ) is a contraction without a non-trivial invariant subspace, then A, $vert A^{n+1}vert^{frac{2}{n+1}}-vert Avert^{2}$ and $vert A^{n+1}vert^{2}- {frac{n+1}{n}}vert Avert^{2}+ 1$ (resp., A, $vert A^{n+1}vert^{frac{2}{n+1}}-vert A^{*}vert^{2}$ and $vert A^{n+2}vert^{2}- {frac{n+1}{n}}vert Avert^{2}+ 1geq0$ ) are proper contractions." @default.
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- W2339992334 date "2016-04-12" @default.
- W2339992334 modified "2023-09-24" @default.
- W2339992334 title "Contractions without non-trivial invariant subspaces satisfying a positivity condition" @default.
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- W2339992334 doi "https://doi.org/10.1186/s13660-016-1058-4" @default.
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