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Bulletin of the Iranian Mathematical Society

, Volume 45, Issue 6, pp 1713–1723 | Cite as

Weighted Composition Lambert-Type Operators via Matrix Representation

  • M. R. Jabbarzadeh
  • M. SohrabiEmail author
Original Paper
  • 20 Downloads

Abstract

In this note, we discuss matrix theoretic characterizations for weighted composition Lambert-type operators of the form \(T_{\varphi }: = M_{w}EM_{u}C_\varphi \) in some operator classes on \(\ell ^2(\mathbb {N}_0),\) such as quasinormal, hyponormal, binormal, n-hyponormal, A-class and\(*\)-A-classes. Also, polar decomposition, Aluthge and mean transform of \(T_\varphi \) will be investigated.

Keywords

Aluthge transformation Mean transform Polar decomposition Matrix representation A-class operator 

Mathematics Subject Classifiation

47B20 47B38 

Notes

Acknowledgements

The author would like to thank the referee for very helpful comments and valuable suggestions.

References

  1. 1.
    Budzynski, P., Jablonski, Z., Jung, I.B., Stochel, J.: Unbounded weighted composition operators in \(L^2\)-spaces. Lecture Notes in Mathematics (2018)Google Scholar
  2. 2.
    Carlson, J.W.: Hyponormal and quasinormal weighted composition operators on \(l^2\). Rocky Mountain J. Math 20, 399–407 (1990)Google Scholar
  3. 3.
    Estaremi, Y., Jabbarzadeh, M.R.: Weighted composition Lambert-type operators on \(L^p\) spaces. Mediterr. J. Math 11, 955–964 (2014)Google Scholar
  4. 4.
    Estaremi, Y., Jabbarzadeh, M.R.: Weighted Lambert-type operators on \(L^p\) spaces. Oper. Matrices 7, 101–116 (2013)Google Scholar
  5. 5.
    Estaremi, Y.: On a class of operators with normal Aluthge transformations. Filomat 29, 1789–1794 (2015)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Furuta, T.: Generalized Aluthge transformation on p-hyponormal operators. Proc. Amer. math. Soc 124, 3071–3075 (1996)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Herron, J.: Weighted conditional expectation operators. Oper. Matrices 5, 107–118 (2011)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Hoover, T., Lambert, A., Quinn, J.: The Markov process determined by a weighted composition operator. Studia Math LXXI I, 225–235 (1982)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Jabbarzadeh, M.R.: Conditional multipliers and essential norm of \(uC_\varphi \) between \(L^p\) spaces. Banach J. Math. Anal 4, 158–168 (2010)Google Scholar
  10. 10.
    Lee, S.H., Lee, W.Y., Yoon, J.: The mean transform of bounded linear operators. J. Math. Anal. Appl 410, 70–81 (2014)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Rao, M.M.: Conditional measure and applications. Marcel Dekker, New York (1993)Google Scholar
  12. 12.
    Singh, R. K., Manhas, J. S.: Composition Operators on Function Spaces. North Holland Math. Studies. 179, Amsterdam (1993)Google Scholar

Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  1. 1.Faculty of Mathematical SciencesUniversity of TabrizTabrizIran
  2. 2.Department of MathematicsLorestan UniversityKhorramabadIran

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