数学季刊 >

2014 , Vol. 29 >Issue 3: 419 - 425

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.03.012

M-亚正规权移位算子与可亚正规权移位算子的一些注记

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  • 1. Department of Mathematics, Harbin Engineering University2. Department of Library, Northeast Forestry University
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.

收稿日期: 2013-02-20

  网络出版日期: 2020-11-30

基金资助

Supported by the NNSF of China(11126286,11201095)； Supported by the Research Fund of Heilongjiang Provincial Education Department(12541618)；

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

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  • 1. Department of Mathematics, Harbin Engineering University2. Department of Library, Northeast Forestry University
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.

Received date: 2013-02-20

  Online published: 2020-11-30

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

本文引用格式

葛斌, 周庆梅 . M-亚正规权移位算子与可亚正规权移位算子的一些注记[J]. 数学季刊, 2014 , 29(3) : 419 -425 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.03.012

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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