Geodesic
On spectral properties of weighted shift operators generated by linear mappings with perron’s conditions
Problemy fiziki, matematiki i tehniki, no. 3 (2012), pp. 43-47

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Weighted shift operators $B$ in the space $L_2 (\mathbb{C}^m )$ generated by a linear mapping $A\colon\mathbb{C}^m \to \mathbb{C}^m$ are considered. A description of properties of $B - \lambda I$ for $\lambda$ belonging to spectrum $\sum(B)$ is given. In particular, the necessary and sufficient condition for $B - \lambda I$ to be one-sided invertible is obtained.
Keywords: weighted shift operators, spectrum, one-sided invertibility, invariant measure, decomposition of oriented graph. 
@article{PFMT_2012_3_a8,
     author = {A. A. Ahmatova},
     title = {On spectral properties of weighted shift operators generated by linear mappings with perron{\textquoteright}s conditions},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {43--47},
     publisher = {mathdoc},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2012_3_a8/}
}
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A. A. Ahmatova. On spectral properties of weighted shift operators generated by linear mappings with perron’s conditions. Problemy fiziki, matematiki i tehniki, no. 3 (2012), pp. 43-47. http://geodesic.mathdoc.fr/item/PFMT_2012_3_a8/