Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

kth-ORDER ESSENTIALLY SLANT WEIGHTED TOEPLITZ OPERATORS

  • Gupta, Anuradha (Department of Mathematics Delhi college of Arts and Commerce University of Delhi) ;
  • Singh, Shivam Kumar (Department of Mathematics University of Delhi)
  • Received : 2018.10.28
  • Accepted : 2018.12.27
  • Published : 2019.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

The notion of $k^{th}$-order essentially slant weighted Toeplitz operator on the weighted Lebesgue space $L^2({\beta})$ is introduced and its algebraic properties are investigated. In addition, the compression of $k^{th}$-order essentially slant weighted Toeplitz operators on the weighted Hardy space $H^2({\beta})$ is also studied.

Keywords

References

  1. P. Aiena, Semi-Fredholm operators, perturbation theory and localized SVEP, XX Escuela Venezolana de Mathematicas, Ed. Ivic, Merida (Venezuela), 2007.
  2. S. C. Arora and J. Bhola, Essentially slant Toeplitz operators, Banach J. Math. Anal. 3 (2009), no. 2, 1-8. https://doi.org/10.15352/bjma/1261086703
  3. S. C. Arora and R. Kathuria, Slant weighted Toeplitz operator, Int. J. Pure Appl. Math. 62 (2010), no. 4, 433-442.
  4. S. C. Arora and R. Kathuria, On weighted Toeplitz operators, Aust. J. Math. Anal. Appl. 8 (2011), no. 1, Art. 11, 10 pp.
  5. S. C. Arora and R. Kathuria, The compression of a slant weighted Toeplitz operator, J. Adv. Res. Pure Math. 4 (2012), no. 4, 48-56. https://doi.org/10.5373/jarpm.1075.081611
  6. J. Barra and P. R. Halmos, Asymptotic Toeplitz operators, Trans. Amer. Math. Soc. 273 (1982), no. 2, 621-630. https://doi.org/10.2307/1999932
  7. G. Datt and N. Ohri, Essentially generalized $\lambda$-slant Toeplitz operators, Tbilisi Math. J. 10 (2017), no. 4, 63-72. https://doi.org/10.1515/tmj-2017-0047
  8. G. Datt and D. K. Porwal, On a generalization of weighted slant Hankel operators, Math. Slovaca 66 (2016), no. 5, 1193-1206. https://doi.org/10.1515/ms-2016-0215
  9. R. G. Douglas, Banach Algebra Techniques in Operator Theory, Academic Press, New York, 1972.
  10. A. Gupta and S. K. Singh, Slant H-Toeplitz operators on the Hardy space, J. Korean Math. Soc. 56 (2019), no. 3, 703-721. https://doi.org/10.4134/JKMS.j180324
  11. M. C. Ho, Properties of slant Toeplitz operators, Indiana Univ. Math. J. 45 (1996), no. 3, 843-862. https://doi.org/10.1512/iumj.1996.45.1973
  12. M. C. Ho, Spectra of slant Toeplitz operators with continuous symbols, Michigan Math. J. 44 (1997), no. 1, 157-166. https://doi.org/10.1307/mmj/1029005627
  13. R. L. Kelley, Weighted shifts on Hilbert space, ProQuest LLC, Ann Arbor, MI, 1966.
  14. V. Lauric, On a weighted Toeplitz operator and its commutant, Int. J. Math. Math. Sci. 2005 (2005), no. 6, 823-835. https://doi.org/10.1155/IJMMS.2005.823
  15. A. L. Shields, Weighted shift operators and analytic function theory, Topics in operator theory, 49-128. Math. Surveys, 13, Amer. Math. Soc., Providence, RI, 1974.