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Reducing subspaces of tensor products of weighted shifts

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Abstract

A unilateral weighted shift A is said to be simple if its weight sequence {α n } satisfies ∇3(α 2 n ) ≠ 0 for all n ≥ 2. We prove that if A and B are two simple unilateral weighted shifts, then A⊗I + I ⊗B is reducible if and only if A and B are unitarily equivalent. We also study the reducing subspaces of A k ⊗ I + I ⊗ B l and give some examples. As an application, we study the reducing subspaces of multiplication operators \(M_{z^k + \alpha w^l }\) on function spaces.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    KunYu Guo & XuDi Wang

  2. School of Sciences, Xi’an University of Technology, Xi’an, 710048, China

    XuDi Wang

Authors
  1. KunYu Guo
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  2. XuDi Wang
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Correspondence to XuDi Wang.

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Guo, K., Wang, X. Reducing subspaces of tensor products of weighted shifts. Sci. China Math. 59, 715–730 (2016). https://doi.org/10.1007/s11425-015-5089-y

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  • DOI: https://doi.org/10.1007/s11425-015-5089-y

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