Classification of multiple unilateral weighted shifts by {\mathbb{A}}_{{\mathrm{\aleph }}_{\mathrm{0}}}

Abstract

In this paper, it is characterized when a multiple unilateral weighted shift belongs to the classes {\mathbb{A}}_n(\mathrm{1}\le n\le {\mathrm{\aleph }}_{\mathrm{0}}). 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.

Key words： Multiple unilateral weighted shifts; classes {\mathbb{A}}_n

References

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