数学季刊 ›› 2014, Vol. 29 ›› Issue (3): 419-425.doi: 10.13371/j.cnki.chin.q.j.m.2014.03.012

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M-亚正规权移位算子与可亚正规权移位算子的一些注记

  

  1. 1. Department of Mathematics, Harbin Engineering University2. Department of Library, Northeast Forestry University
  • 收稿日期:2013-02-20 出版日期:2014-09-30 发布日期:2020-11-30
  • 作者简介:GE Bin(1979-), male, native of Harbin, Heilongjiang, an associate professor of Harbin Engineering University, Ph.D., engages in operator theory; ZHOU Qing-mei(1982-), female, native of Harbin, Heilongjiang, a lecturer of Northeast Forestry University, M.S.D., engages in operator theory.
  • 基金资助:
    Supported by the NNSF of China(11126286,11201095)； Supported by the Research Fund of Heilongjiang Provincial Education Department(12541618)；

Some Notes on M-hyponormal Weighted Shifts and Hyponormalizable Weighted Shifts

  1. 1. Department of Mathematics, Harbin Engineering University2. Department of Library, Northeast Forestry University
  • Received:2013-02-20 Online:2014-09-30 Published:2020-11-30
  • About author:GE Bin(1979-), male, native of Harbin, Heilongjiang, an associate professor of Harbin Engineering University, Ph.D., engages in operator theory; ZHOU Qing-mei(1982-), female, native of Harbin, Heilongjiang, a lecturer of Northeast Forestry University, M.S.D., engages in operator theory.
  • Supported by:
    Supported by the NNSF of China(11126286,11201095)； Supported by the Research Fund of Heilongjiang Provincial Education Department(12541618)；

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摘要： 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. 

关键词: M-hyponormal, unilateral weighted shifts, spectral radius, positive operator

Abstract: 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. 

Key words: M-hyponormal, unilateral weighted shifts, spectral radius, positive operator

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