Abstract In this paper, it is characterized when a multiple unilateral weighted shift belongs to the classes An （1 ≤ n ≤ x0）. As a result, we perfect and generalize the previous conclusions given by H. Bercovici, ...Abstract In this paper, it is characterized when a multiple unilateral weighted shift belongs to the classes An （1 ≤ n ≤ x0）. 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.展开更多
A unilateral weighted shift A is said to be simple if its weight sequence {α_n} satisfies ▽~3(α_n^2)≠0for all n≥2.We prove that if A and B are two simple unilateral weighted shifts,then AI+IB is reducible if and ...A unilateral weighted shift A is said to be simple if its weight sequence {α_n} satisfies ▽~3(α_n^2)≠0for all n≥2.We prove that if A and B are two simple unilateral weighted shifts,then AI+IB is reducible if and only if A and B are unitarily equivalent.We also study the reducing subspaces of A^kI+IB^l and give some examples.As an application,we study the reducing subspaces of multiplication operators Mzk+αωl on function spaces.展开更多
It is shown in[6]and[7]that a necessary and sufficient condition for a hyponormal weightedunilateral shift to be unitarily equivalent to a Toeplitz operator is that its weights satisfy(1-|an|2)=(1-|a0|2)(1-|an-1|2)n≥...It is shown in[6]and[7]that a necessary and sufficient condition for a hyponormal weightedunilateral shift to be unitarily equivalent to a Toeplitz operator is that its weights satisfy(1-|an|2)=(1-|a0|2)(1-|an-1|2)n≥1,where ansatisfiesan=1.In[8],the author obtainedsimilar result for the hyponormal weighted unilateral shift of multiplicity 2.The aim of this展开更多
文摘Abstract In this paper, it is characterized when a multiple unilateral weighted shift belongs to the classes An （1 ≤ n ≤ x0）. 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.
基金supported by National Natural Science Foundation of China(Grant Nos.11371096 and 11471113)
文摘A unilateral weighted shift A is said to be simple if its weight sequence {α_n} satisfies ▽~3(α_n^2)≠0for all n≥2.We prove that if A and B are two simple unilateral weighted shifts,then AI+IB is reducible if and only if A and B are unitarily equivalent.We also study the reducing subspaces of A^kI+IB^l and give some examples.As an application,we study the reducing subspaces of multiplication operators Mzk+αωl on function spaces.
基金This research was supported in part by a Foundation from Academy of Sciences of China.
文摘It is shown in[6]and[7]that a necessary and sufficient condition for a hyponormal weightedunilateral shift to be unitarily equivalent to a Toeplitz operator is that its weights satisfy(1-|an|2)=(1-|a0|2)(1-|an-1|2)n≥1,where ansatisfiesan=1.In[8],the author obtainedsimilar result for the hyponormal weighted unilateral shift of multiplicity 2.The aim of this
