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

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.

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 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 https://doi.org/10.1090/S0002-9947-1982-0667164-X
  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 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 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 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 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 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 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.