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arXiv · 1303.1293

Operators generated by Morse-Smale mappings

A. Antonevich·J. Makowska
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Abstract

Weighted shift operators $B$ in space $L^2(X,\mu)$ that are induced by Morse-Smale type of mappings are considered. A description of the properties of $B-\lambda I$ for $\lambda$ belonging to spectrum $\Sigma(B)$ is given. In particular, there is the necessary and sufficient condition that $B-\lambda I$ be a one-sided invertible and the condition that set $Im(B-\lambda I)$ be non-closed. These conditions use a new notation: an oriented decomposition of oriented graph $G(X,\alpha)$ generated by mapping $\alpha$

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A. Antonevich, J. Makowska. 2013-03-06. Operators generated by Morse-Smale mappings. https://arxiv.org/abs/1303.1293

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