Classification of multiple unilateral weighted shifts by $\mathbb{A}_{\aleph _0 }$

Abstract

In this paper, it is characterized when a multiple unilateral weighted shift belongs to the classes $\mathbb{A}_n \left( {1 \leqslant n \leqslant \aleph _0 } \right)$. As a result, we perfect and generalize the previous conclusions given by H. Bercovici, C. Foias, and C. Pearcy. Moreover, we remark that Question 21 posed by Shields has been negatively answered.

Keywords

Multiple unilateral weighted shifts / classes $\mathbb{A}_n$

References

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