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
Let {an}∞n=0be a weight sequence and let W denote the associated unilateral weighted shift on H. In this paper, we consider the connection between the M-hyponormal and hyponormalizable weighted shift operator. Main r...Let {an}∞n=0be a weight sequence and let W denote the associated unilateral weighted shift on H. In this paper, we consider the connection between the M-hyponormal and hyponormalizable weighted shift operator. Main results are Theorems 4.1 and Theorems4.2. Theorem 4.1 gives the sufficient condition that a weighted shifts M-hyponormal operator is hyponormalizable. Theorem 4.2 gives the sufficient condition that a hyponormalizable weighted shift operator is M-hyponormal. Finally, invariant subspaces of such operators are discussed.展开更多
Extending previous results of Grosse-Erdmann and Peris we obtain a characterization of chaotic unilateral weighted backward shifts on sequentially complete topological sequence spaces in which the canonical unit vecto...Extending previous results of Grosse-Erdmann and Peris we obtain a characterization of chaotic unilateral weighted backward shifts on sequentially complete topological sequence spaces in which the canonical unit vectors(e_(n))_(n=1)^(∞) form an unconditional basis.展开更多
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
基金Supported by the NNSF of China(11126286,11201095)Supported by the Research Fund of Heilongjiang Provincial Education Department(12541618)
文摘Let {an}∞n=0be a weight sequence and let W denote the associated unilateral weighted shift on H. In this paper, we consider the connection between the M-hyponormal and hyponormalizable weighted shift operator. Main results are Theorems 4.1 and Theorems4.2. Theorem 4.1 gives the sufficient condition that a weighted shifts M-hyponormal operator is hyponormalizable. Theorem 4.2 gives the sufficient condition that a hyponormalizable weighted shift operator is M-hyponormal. Finally, invariant subspaces of such operators are discussed.
基金Supported by Research Program of Science at Universities of Inner Mongolia Autonomous Region(Grant No.NJZY22328)。
文摘Extending previous results of Grosse-Erdmann and Peris we obtain a characterization of chaotic unilateral weighted backward shifts on sequentially complete topological sequence spaces in which the canonical unit vectors(e_(n))_(n=1)^(∞) form an unconditional basis.
