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

GE Bin, ZHOU Qing-mei

doi:10.13371/j.cnki.chin.q.j.m.2014.03.012

Chinese Quarterly Journal of Mathematics >

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

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

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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Abstract

Let {a_n}^∞_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

Cite this article

GE Bin, ZHOU Qing-mei . Some Notes on M-hyponormal Weighted Shifts and Hyponormalizable Weighted Shifts[J]. Chinese Quarterly Journal of Mathematics, 2014 , 29(3) : 419 -425 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.03.012

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