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
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摘要
Cuckovic等刻画了shift算子加上Volterra算子在Hardy-Hilbert空间上的不变子空间。在他们以及Stessin等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Hardy空间上的不变子空间及约化子空间,部分地推广了他们的结论。
The invariant subspaces of the shift operator plus Volterra operator on Hardy-Hilbert space were depicted by Cuckovic. Base on the reports of the reducing subspaces by Stessin and other experts, the invariant subspaces and reducing subspaces of weighted shift operators plus Volterra type operators on Hardy spaces are studied in this paper, and partial conclusions were generalized.
The invariant subspaces of the shift operator plus Volterra operator on Hardy-Hilbert space were depicted by Cuckovic. Base on the reports of the reducing subspaces by Stessin and other experts, the invariant subspaces and reducing subspaces of weighted shift operators plus Volterra type operators on Hardy spaces are studied in this paper, and partial conclusions were generalized.
引文
[1]BERNSTEIN A,ROBINSON A.Solution of an invariant subspace problem of K.T.Smith and P.R.Halmos[J].Pacific Journal of Mathematics,1966,16(3):421-431.
[2]HALMOS P.Invariant subspaces of polynomially compact operators[J].Pacific Journal of Mathematics,1966,16(3):433-437.
[3]CHALENDER I,PARTINGTON J.Modern approaches to the invariant-subspace problem[M].Cambridge:Cambridge University Press,2011.
[4]BEURLING A.On two problems concerning linear transformations in Hilbert space[J].Acta Mathematica,1949,81(1):239-255.
[5]LIN Q Z,LIU J M,WU Y T.Volterra type operators on Sp(D)spaces[J].Journal of Mathematical Analysis and Applications,2018,461(2):1100-1114.
[6]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.
[7]STESSIN M,ZHU K H.Reducing subspaces of weighted shift operator[J].Proceedings of the American Mathematical Society,2002,130(9):2631-2639.
[8]ZHAO L K.Reducing subspaces for a class of multiplication operators on the Dirichlet space[J].Proceedings of the American Mathematical Society,2009,137(9):3091-3097.
[9]LUO S B.Reducing subspaces of multiplication operators on the Dirichlet space[J].Integral Equations and Operator Theory,2016,85(4):539-554.
[10]ALEMAN A,CIMA J.An integral operator on Hpand Hardy’s inequality[J].Journal d'Analyse Mathematique,2001,85(1):157-176.
[11]ALEMAN A,SISKAKIS A.An integral operator on Hp[J].Complex Variables Theory and Application,1995,28(2):149-158.
[12]ALEMAN A,SISKAKIS A.Integration operators on Bergman spaces[J].Indiana University Mathematics Journal,1997,46(2):337-356.
[13]ALEMAN A,KORENBLUM B.Volterra invariant subspaces of Hp[J].Bulletin des Sciences Mathematiques,2008,132(6):510-528.
[2]HALMOS P.Invariant subspaces of polynomially compact operators[J].Pacific Journal of Mathematics,1966,16(3):433-437.
[3]CHALENDER I,PARTINGTON J.Modern approaches to the invariant-subspace problem[M].Cambridge:Cambridge University Press,2011.
[4]BEURLING A.On two problems concerning linear transformations in Hilbert space[J].Acta Mathematica,1949,81(1):239-255.
[5]LIN Q Z,LIU J M,WU Y T.Volterra type operators on Sp(D)spaces[J].Journal of Mathematical Analysis and Applications,2018,461(2):1100-1114.
[6]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.
[7]STESSIN M,ZHU K H.Reducing subspaces of weighted shift operator[J].Proceedings of the American Mathematical Society,2002,130(9):2631-2639.
[8]ZHAO L K.Reducing subspaces for a class of multiplication operators on the Dirichlet space[J].Proceedings of the American Mathematical Society,2009,137(9):3091-3097.
[9]LUO S B.Reducing subspaces of multiplication operators on the Dirichlet space[J].Integral Equations and Operator Theory,2016,85(4):539-554.
[10]ALEMAN A,CIMA J.An integral operator on Hpand Hardy’s inequality[J].Journal d'Analyse Mathematique,2001,85(1):157-176.
[11]ALEMAN A,SISKAKIS A.An integral operator on Hp[J].Complex Variables Theory and Application,1995,28(2):149-158.
[12]ALEMAN A,SISKAKIS A.Integration operators on Bergman spaces[J].Indiana University Mathematics Journal,1997,46(2):337-356.
[13]ALEMAN A,KORENBLUM B.Volterra invariant subspaces of Hp[J].Bulletin des Sciences Mathematiques,2008,132(6):510-528.