On Quasi-similarity of Multiplication Operator on the Weighted Bergman Space in the Unit Ball

Cui CHEN, Ya WANG, Yu Xia LIANG

Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (3) : 455-460.

PDF(375 KB)
PDF(375 KB)
Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (3) : 455-460. DOI: 10.12386/A2022sxxb0037

On Quasi-similarity of Multiplication Operator on the Weighted Bergman Space in the Unit Ball

  • Cui CHEN1, Ya WANG1, Yu Xia LIANG2
Author information +
History +

Abstract

For α>1, let Aα2(BN) be the weighted Bergman space on the unit ball BN in CN. We prove that the multiplication operator Mzn is quasi-similar to 1i=1NniMz on Aα2(BN) for the multi-index n=(n1,n2,,nN).

Key words

multiplication operator / weighted Bergman space / quasi-similarity

Cite this article

Download Citations
Cui CHEN, Ya WANG, Yu Xia LIANG. On Quasi-similarity of Multiplication Operator on the Weighted Bergman Space in the Unit Ball. Acta Mathematica Sinica, Chinese Series, 2022, 65(3): 455-460 https://doi.org/10.12386/A2022sxxb0037

References

[1] Ahmadi M. F., Hedayatian K., On similarity of powers of shift operators, Turk. J. Math., 2012, 36: 596–600.
[2] Alfonso M. R., Manuel P. E., Invariant subspaces of parabolic self-maps in the Dirichlet space, J. Funct. Anal., 2014, 266: 4115–4120.
[3] Alfonso M. R., Manuel P. E., Stanislav A. S., Invariant subspaces of parabolic self-maps in the Hardy space, Math. Res. Lett., 2010, 17(1): 99–107.
[4] Chen Y., Qin C. T., Wu Q., Reducibility and unitary equivalence of analytic multipliers on Sobolev disk algebra, J. Math. Anal. Appl., 2017, 455(2): 1249–1256.
[5] Čučković Ž., Paudyal B., Invariant subspaces of the shift plus complex Volterra operator, J. Math. Anal. Appl., 2015, 426: 1174–1181.
[6] Douglas R. G., Kim Y. S., Reducing subspaces on the annulus, Integr. Equat. Oper. Th., 2011, 70: 1–15.
[7] Ji K., Shi R., Similarity of multiplication operators on the Sobolev disk algebra, Acta Math. Sin. Engl. Ser., 2013, 29(4): 789–800.
[8] Jiang C. L., Li Y. C., The commutant and similarity invariant of analytic Toeplitz operators on Bergman space, Sci. China Ser. A, 2007, 50(5): 651–664.
[9] Jiang C. L., Zheng D. C., Similarity of analytic Toeplitz operators on the Bergman spaces, J. Funct. Anal., 2010, 258: 2961–2982.
[10] Li Y. C., On similarity of multiplication operator on weighted Bergman space, Integr. Equat. Oper. Th., 2009, 63: 95–102.
[11] Li Y. C., Lan W. H., Liu J. L., On quasi-similarity and reducing subspaces of multiplication operator on the Fock space, J. Math. Anal. Appl., 2014, 409: 899–905.
[12] Li Y. C., Liu Q. J., Lan W. H., On similarity and reducing subspaces of multiplication operator on Sobolev disk algebra, J. Math. Anal. Appl., 2014, 419: 1161–1167.
[13] Zhao R. F., A similarity invariant and the commutant of some multiplication operators on the Sobolev disk algebra, Int. J. Math. Math. Sci., 2012, Artical ID 378217, 17 pp.
PDF(375 KB)

464

Accesses

0

Citation

Detail

Sections
Recommended

/