Operators generated by Morse-Smale mappings
Abstract
Weighted shift operators B in space L2(X,μ) that are induced by Morse-Smale type of mappings are considered. A description of the properties of B-λ I for λ belonging to spectrum (B) is given. In particular, there is the necessary and sufficient condition that B-λ I be a one-sided invertible and the condition that set Im(B-λ I) be non-closed. These conditions use a new notation: an oriented decomposition of oriented graph G(X,α) generated by mapping α
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