On similarity of powers of shift operators

Authors: MASOUMEH FAGHIH AHMADI, KARIM HEDAYATIAN

Abstract: Let M_z and B denote, respectively, the multiplication operator and the backward shift operator on a weighted Hardy space. We present sufficient conditions so that M_{z^n} is similar to \bigoplus_1^nM_z, and B^n is similar to \bigoplus_1^nB. The first part generalizes a result obtained by Yucheng Li.

Keywords: Weighted Hardy space, multiplication operator, similarity

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