Browse > Article
http://dx.doi.org/10.14317/jami.2021.443

ON n-HYPONOHRMALITY FOR BACKWARD EXTENSIONS OF BERGMAN WEIGHTED SHIFTS  

DONG, YANWU (Department of Mathematics, Zhanjiang Preschool Education College(Fundamental Education College of Lingnan Normal University))
ZHENG, GUIJUN (Department of Mathematics, Zhanjiang Preschool Education College(Fundamental Education College of Lingnan Normal University))
LI, CHUNJI (Department of Mathematics, Northeastern University)
Publication Information
Journal of applied mathematics & informatics / v.39, no.3_4, 2021 , pp. 443-454 More about this Journal
Abstract
In this paper, we discuss the backward extensions of Bergman shifts Wα(m), where $${\alpha}(m)\;:\;\sqrt{\frac{m}{m+1}},\;{\sqrt{\frac{m+1}{m+2}}},\;{\cdots},\;(m{\in}\mathbb{N})$$. We obtained a complete description of the n-hynonormality for backward one, two and three step extensions.
Keywords
subnormal; hyponormal; n-hynonormal; weighted shifts;
Citations & Related Records
연도 인용수 순위
  • Reference
1 MacKichan Software, Inc. Scientific WorkPlace, Version 4.0, MacKichan Software, Inc. 2002.
2 C. Li, Hyponormal weighted shift operators and complex moment problems, Ph.D. Thesis, Kyungpook Nat. Univ. 1999.
3 C. Li, W. Qi and H. Wang, Backward extensions of Bergman-type weighed shift, Bull. Korean Math. Soc. 57 (2020), 81-93.   DOI
4 G. Exner, J.Y. Jin, I.B. Jung and J.E. Lee, Weak Hamburger-type weighted shifts and their examples, J. Math. Anal. Appl. 462 (2018), 1357-1380.   DOI
5 R. Curto and L. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, Integral Equations Operator Theory 17 (1993), 202-246.   DOI
6 R. Curto and L. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, II, Integral Equations and Operator Theory 18 (1994), 369-426.   DOI
7 Y. Dong, M.R. Lee and C. Li, New results on k-hyponormality of backward extensions of subnormal weighted shifts, J. Appl. Math. & Informatics 37 (2019), 73-83.   DOI
8 Y.B. Choi, J.K. Han and W.Y. Lee, One-step extension of the Bergman shift, Proc. Amer. Math. Soc. 128 (2000), 3639-3646.   DOI
9 R. Curto, Joint hyponormality:A bridge between hyponormality and subnormality, Proc. Sym. Math. 51 (1990), 69-91.   DOI
10 I.B. Jung and C. Li, Backward extensions of hyponormal weighted shifts, Math. Japonica 52 (2000), 267-278.
11 J. Stampfli, Which weighted shifts are subnormal, Pacific J. Math. 17 (1966), 367-379.   DOI
12 I.B. Jung and C. Li, A formula for k-hyponormality of backstep extensions of subnormal weighted shifts, Proc. Amer. Math. Soc. 129 (2001), 2343-2351.   DOI
13 C. Li and M.R. Lee, Existence of non-subnormal completely semi-weakly hyponormal weighted shifts, Filomat 31 (2017), 1627-1638.   DOI
14 C. Li, M.R. Lee and S. Baek, A relationship:subnormal, polynomially hyponormal and semi-weakly hyponormal weighted shifts, J. Math. Anal. Appl. 479 (2019), 703-717.   DOI
15 C. Li and W. Qi, Formulae of k-hyponormality of backward extensions of Bergman shifts, J. Appl. & Pure Math. 1 (2019), 131-140.