Power Set of Some Quasinilpotent Weighted Shifts
Sign Up to like & getrecommendations! Published in 2021 at "Integral Equations and Operator Theory"
DOI: 10.1007/s00020-021-02633-9
Abstract: For a quasinilpotent bounded linear operator T, we write $$k_x=\limsup \limits _{z\rightarrow 0}\frac{\log \Vert (z-T)^{-1}x\Vert }{\log \Vert (z-T)^{-1}\Vert }$$ for each nonzero vector x. Set $$\Lambda (T)=\{k_x:x\ne 0\}$$ , and call it the power set… read more here.
Keywords: vert; tau; lambda; power set ... See more keywords
On quasinilpotent operators and the invariant subspace problem
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2019.04.026
Abstract: We show that a bounded quasinilpotent operator $T$ acting on an infinite dimensional Banach space has an invariant subspace if and only if there exists a rank one operator $F$ and a scalar $\alpha\in\mathbb{C}$, $\alpha\neq… read more here.
Keywords: quasinilpotent operators; operators invariant; quasinilpotent; invariant subspace ... See more keywords