Coherent local hyperbolicity of a linear extension and the essential spectra of a weighted shift operator on a closed interval (Q2571489)

In this paper, weighted shift operators \(B\) generated by diffeomorphisms of a closed interval are considered on \(L_p\) spaces. The notion of coherent local hyperbolicity of the associated linear extension is introduced, and it is established that the closedness of the range of the operator \(I- B\) is equivalent to coherent local hypercyclicity. On the basis of this result, the description of some essential spectra of the operator \(B\) is also given.