Acknowledgement
The first and second authors were supported by key scientific research projects in Zhanjiang Preschool Education College(ZJYZZD201801).
References
- 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. https://doi.org/10.1090/S0002-9939-00-05516-7
- R. Curto, Joint hyponormality:A bridge between hyponormality and subnormality, Proc. Sym. Math. 51 (1990), 69-91. https://doi.org/10.1090/pspum/051.2/1077422
- R. Curto and L. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, Integral Equations Operator Theory 17 (1993), 202-246. https://doi.org/10.1007/BF01200218
- R. Curto and L. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, II, Integral Equations and Operator Theory 18 (1994), 369-426. https://doi.org/10.1007/BF01200183
- 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. https://doi.org/10.14317/JAMI.2019.073
- 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. https://doi.org/10.1016/j.jmaa.2018.02.045
- I.B. Jung and C. Li, Backward extensions of hyponormal weighted shifts, Math. Japonica 52 (2000), 267-278.
- 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. https://doi.org/10.1090/S0002-9939-00-05844-5
- C. Li, Hyponormal weighted shift operators and complex moment problems, Ph.D. Thesis, Kyungpook Nat. Univ. 1999.
- C. Li and M.R. Lee, Existence of non-subnormal completely semi-weakly hyponormal weighted shifts, Filomat 31 (2017), 1627-1638. https://doi.org/10.2298/FIL1706627L
- 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. https://doi.org/10.1016/j.jmaa.2019.06.046
- C. Li and W. Qi, Formulae of k-hyponormality of backward extensions of Bergman shifts, J. Appl. & Pure Math. 1 (2019), 131-140.
- C. Li, W. Qi and H. Wang, Backward extensions of Bergman-type weighed shift, Bull. Korean Math. Soc. 57 (2020), 81-93. https://doi.org/10.4134/BKMS.b190060
- J. Stampfli, Which weighted shifts are subnormal, Pacific J. Math. 17 (1966), 367-379. https://doi.org/10.2140/pjm.1966.17.367
- MacKichan Software, Inc. Scientific WorkPlace, Version 4.0, MacKichan Software, Inc. 2002.