加权Bergman空间上的加权shift算子加上Volterra型算子的不变子空间
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摘要
Cuckovic等刻画了shift算子加上整数倍Volterra算子在Hardy空间上的不变子空间。在他们以及Stessin和Zhu的关于约化子空间的研究基础上,文章研究了加权shift算子加上Volterra型算子在加权Bergman空间上的不变子空间问题并给出其所有约化子空间的完整刻画。
Cuckovic et al. characterized the invariant subspaces of the shift operator plus integer multiple of Volterra operator on Hardy spaces. Inspired by their works and the studies of the reducing subspaces by Stessin and Zhu, in this paper,the invariant subspaces and the reducing subspaces of weighted shift operators plus Volterra type operators on weighted Bergman spaces were studied.
Cuckovic et al. characterized the invariant subspaces of the shift operator plus integer multiple of Volterra operator on Hardy spaces. Inspired by their works and the studies of the reducing subspaces by Stessin and Zhu, in this paper,the invariant subspaces and the reducing subspaces of weighted shift operators plus Volterra type operators on weighted Bergman spaces were studied.
引文
[1]林庆泽.关于Hilbert空间的不变子空间问题[J].乐山师范学院学报,2018,33(8):1-3.
[2] BEURLING A. On two problems concerning linear transformations in Hilbert space[J]. Acta Mathematica,1949,81(1):239-255.
[3] DUREN P,SCHUSTER A. Bergman spaces[M]. New York:American Mathematical Society,2004.
[4] ZHU K. Operator theory in function spaces[M]. New York:American Mathematical Society,2007.
[5] CUCKOVIC Z,PAUDYAL B. Invariant subspaces of the shift plus complex Volterra operator[J]. Journal of Mathematical Analysis and Applications,2015,426(2):1174-1181.
[6] LIN Q,LIU J,WU Y. Volterra type operators on Sp(D)spaces[J]. Journal of Mathematical Analysis and Applications,2018,461(2):1100-1114.
[7] CUCKOVIC Z,PAUDYAL B. The lattices of invariant subspaces of a class of operators on the Hardy space[J]. Archiv der Mathe?matik,2018,110(5):477-486.
[8] LIN Q. The invariant subspaces of the shift plus integer multiple of the Volterra operator on Hardy spaces[J]. Archiv der Mathema?tik,2018,111(5):513–522.
[9] STESSIN M,ZHU K. Reducing subspaces of weighted shift operator[J]. Proceedings of the American Mathematical Society,2002,130(9):2631-2639.
[10] ZHAO L. Reducing subspaces for a class of multiplication operators on the Dirichlet space[J]. Proceedings of the American Math?ematical Society,2009,137(9):3091-3097.
[11] LUO S. Reducing subspaces of multiplication operators on the Dirichlet space[J]. Integral Equations Operator Theory,2016,85(4):539-554.
[12] ALEMAN A,CIMA J. An integral operator on Hpand Hardy’s inequality[J]. Journal d'Analyse Mathematique,2001,85(1):157-176.
[13] ALEMAN A,SISKAKIS A. An integral operator on Hp[J]. Complex Variables Theory and Application,1995,28(2):149-158.
[14] ALEMAN A, SISKAKIS A. Integration operators on Bergman spaces[J]. Indiana University Mathematics Journal,1997,46(2):337-356.
[15] ALEMAN A,KORENBLUM B. Volterra invariant subspaces of Hp[J]. Bulletin des Sciences Mathematiques,2008,132(6):510-528.
[16]林庆泽.加权shift算子加上Volterra型算子在Hardy空间上的不变子空间及约化子空间[J].海南师范大学学报(自然科学版),2018,31(3):291-294.
[17]林庆泽. Shift算子加上整数倍Volterra算子在加权Bergman空间上的不变子空间[J].海南师范大学学报(自然科学版),2018,31(4):391-396.
[18] LI Y,CHEN H,LAN W. On similarity and reducing subspaces of the n-shift plus certain weighted Volterra operator[J]. Journal of Function Spaces,2017,4(1):1-8.
[2] BEURLING A. On two problems concerning linear transformations in Hilbert space[J]. Acta Mathematica,1949,81(1):239-255.
[3] DUREN P,SCHUSTER A. Bergman spaces[M]. New York:American Mathematical Society,2004.
[4] ZHU K. Operator theory in function spaces[M]. New York:American Mathematical Society,2007.
[5] CUCKOVIC Z,PAUDYAL B. Invariant subspaces of the shift plus complex Volterra operator[J]. Journal of Mathematical Analysis and Applications,2015,426(2):1174-1181.
[6] LIN Q,LIU J,WU Y. Volterra type operators on Sp(D)spaces[J]. Journal of Mathematical Analysis and Applications,2018,461(2):1100-1114.
[7] CUCKOVIC Z,PAUDYAL B. The lattices of invariant subspaces of a class of operators on the Hardy space[J]. Archiv der Mathe?matik,2018,110(5):477-486.
[8] LIN Q. The invariant subspaces of the shift plus integer multiple of the Volterra operator on Hardy spaces[J]. Archiv der Mathema?tik,2018,111(5):513–522.
[9] STESSIN M,ZHU K. Reducing subspaces of weighted shift operator[J]. Proceedings of the American Mathematical Society,2002,130(9):2631-2639.
[10] ZHAO L. Reducing subspaces for a class of multiplication operators on the Dirichlet space[J]. Proceedings of the American Math?ematical Society,2009,137(9):3091-3097.
[11] LUO S. Reducing subspaces of multiplication operators on the Dirichlet space[J]. Integral Equations Operator Theory,2016,85(4):539-554.
[12] ALEMAN A,CIMA J. An integral operator on Hpand Hardy’s inequality[J]. Journal d'Analyse Mathematique,2001,85(1):157-176.
[13] ALEMAN A,SISKAKIS A. An integral operator on Hp[J]. Complex Variables Theory and Application,1995,28(2):149-158.
[14] ALEMAN A, SISKAKIS A. Integration operators on Bergman spaces[J]. Indiana University Mathematics Journal,1997,46(2):337-356.
[15] ALEMAN A,KORENBLUM B. Volterra invariant subspaces of Hp[J]. Bulletin des Sciences Mathematiques,2008,132(6):510-528.
[16]林庆泽.加权shift算子加上Volterra型算子在Hardy空间上的不变子空间及约化子空间[J].海南师范大学学报(自然科学版),2018,31(3):291-294.
[17]林庆泽. Shift算子加上整数倍Volterra算子在加权Bergman空间上的不变子空间[J].海南师范大学学报(自然科学版),2018,31(4):391-396.
[18] LI Y,CHEN H,LAN W. On similarity and reducing subspaces of the n-shift plus certain weighted Volterra operator[J]. Journal of Function Spaces,2017,4(1):1-8.