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Year 2017, Volume: 5 Issue: 1, 70 - 76, 30.04.2017
https://doi.org/10.36753/mathenot.421702

Abstract

References

  • [1] Angus E. Taylor, David C. Lay, Introduction to Functional Analysis, R.E. Krieger Publishing Company, 1980.
  • [2] A. Kufner, O. John and S. Fucik, Function Spaces, Academia Prague, 1977.
  • [3] B. Aupetit, A Primer on Spectral Theory, Springer-verlag, Newyork, 1991.
  • [4] B. S. Komal and S. Gupta, Composition operators on Orlicz spaces, Indian J. Pure Apply. Math., 32 (2001), 1117-1122.
  • [5] E. Nordgren, Composition Operator On Hilbert Spaces, Lecture Notes on Mathematics, 693, 37-68, SpringerVerlag, Newyork, 1978.
  • [6] F. Riesz, Uber lineare Functionalgleichungen, Acta Math. 41 (1918), 71-98.
  • [7] H. Hudzik and L. Malingranda, Amemiya norm equals Orlicz norm in general, Indag. Math. N. S., 11 (2000), 573-585.
  • [8] H. Nakano, Generalized modular spaces, Studia Math., 31 (1968), 440-449.
  • [9] J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Math. 1034, Springer, Berlinn 1983.
  • [10] J. Musielak and W. Orlicz, On Modular Spaces, Studia math., 18 (1959), 49-65.
  • [11] M. A. Krasnoselskii and Ya. B. Rutickii, Convex function and Orlicz spaces, Noordhorff, Groningen, 1961.
  • [12] M. Burgos, A. Kaidi, M. Mbekhta and M. Oudghiri, The Descent Spectrum and Perturbations, J. Operator Theory, 56 (2006), no. 2, 259-271.
  • [13] M. M. Rao and Z. D. Ren, Theory of Orlicz spaces, Marcel Dekker, New York, 1991.
  • [14] R. K. Sing and J. S. Manhas, Composition operator on function spaecs, North-Holland Mathematics Studies 179, Newyork, 1993.
  • [15] Rajeev Kumar, Ascent and descent of weighted composition operators on L^p-spaces, Mathematicki Vensik, 60 (2008), no. 1, 47-51.
  • [16] Romesh Kumar, Composition operator on Oricz spaces, Integr. equ. Oper. Theory., 29 (1997), 17-22.
  • [17] V. De. Cicoo and G. Marino, Composition Operator On Summable functions spaces, Le Mathematiche XLIV, (1989), 3-20.
  • [18] W. Luxemburg, Banach Function Spaces, Thesis, Technische Hogeschool te Delft, Netherland, 1955.
  • [19] Y. A. Abramovich and C. D. Aliprantis, An Invitation to Operator Theory, Graduate Studies in Mathematics 50, American Mathematical Society, 2002.
  • [20] Y. Cui, H. Hudzik, R. Kumar and L. Maligranda, Composition operators in Orlicz Spaces, J. Aust. Math. Soc., 76 (2004), 189-206.

On the Properties of Ascent and Descent of Composition Operator on Orlicz Spaces

Year 2017, Volume: 5 Issue: 1, 70 - 76, 30.04.2017
https://doi.org/10.36753/mathenot.421702

Abstract

Here, the composition operators on Orlicz spaces with finite ascent and descent as well as infinite ascent
and descent are characterized.

References

  • [1] Angus E. Taylor, David C. Lay, Introduction to Functional Analysis, R.E. Krieger Publishing Company, 1980.
  • [2] A. Kufner, O. John and S. Fucik, Function Spaces, Academia Prague, 1977.
  • [3] B. Aupetit, A Primer on Spectral Theory, Springer-verlag, Newyork, 1991.
  • [4] B. S. Komal and S. Gupta, Composition operators on Orlicz spaces, Indian J. Pure Apply. Math., 32 (2001), 1117-1122.
  • [5] E. Nordgren, Composition Operator On Hilbert Spaces, Lecture Notes on Mathematics, 693, 37-68, SpringerVerlag, Newyork, 1978.
  • [6] F. Riesz, Uber lineare Functionalgleichungen, Acta Math. 41 (1918), 71-98.
  • [7] H. Hudzik and L. Malingranda, Amemiya norm equals Orlicz norm in general, Indag. Math. N. S., 11 (2000), 573-585.
  • [8] H. Nakano, Generalized modular spaces, Studia Math., 31 (1968), 440-449.
  • [9] J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Math. 1034, Springer, Berlinn 1983.
  • [10] J. Musielak and W. Orlicz, On Modular Spaces, Studia math., 18 (1959), 49-65.
  • [11] M. A. Krasnoselskii and Ya. B. Rutickii, Convex function and Orlicz spaces, Noordhorff, Groningen, 1961.
  • [12] M. Burgos, A. Kaidi, M. Mbekhta and M. Oudghiri, The Descent Spectrum and Perturbations, J. Operator Theory, 56 (2006), no. 2, 259-271.
  • [13] M. M. Rao and Z. D. Ren, Theory of Orlicz spaces, Marcel Dekker, New York, 1991.
  • [14] R. K. Sing and J. S. Manhas, Composition operator on function spaecs, North-Holland Mathematics Studies 179, Newyork, 1993.
  • [15] Rajeev Kumar, Ascent and descent of weighted composition operators on L^p-spaces, Mathematicki Vensik, 60 (2008), no. 1, 47-51.
  • [16] Romesh Kumar, Composition operator on Oricz spaces, Integr. equ. Oper. Theory., 29 (1997), 17-22.
  • [17] V. De. Cicoo and G. Marino, Composition Operator On Summable functions spaces, Le Mathematiche XLIV, (1989), 3-20.
  • [18] W. Luxemburg, Banach Function Spaces, Thesis, Technische Hogeschool te Delft, Netherland, 1955.
  • [19] Y. A. Abramovich and C. D. Aliprantis, An Invitation to Operator Theory, Graduate Studies in Mathematics 50, American Mathematical Society, 2002.
  • [20] Y. Cui, H. Hudzik, R. Kumar and L. Maligranda, Composition operators in Orlicz Spaces, J. Aust. Math. Soc., 76 (2004), 189-206.
There are 20 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Ratan Kumar Giri This is me

Shesadev Pradhan This is me

Publication Date April 30, 2017
Submission Date October 5, 2016
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Giri, R. K., & Pradhan, S. (2017). On the Properties of Ascent and Descent of Composition Operator on Orlicz Spaces. Mathematical Sciences and Applications E-Notes, 5(1), 70-76. https://doi.org/10.36753/mathenot.421702
AMA Giri RK, Pradhan S. On the Properties of Ascent and Descent of Composition Operator on Orlicz Spaces. Math. Sci. Appl. E-Notes. April 2017;5(1):70-76. doi:10.36753/mathenot.421702
Chicago Giri, Ratan Kumar, and Shesadev Pradhan. “On the Properties of Ascent and Descent of Composition Operator on Orlicz Spaces”. Mathematical Sciences and Applications E-Notes 5, no. 1 (April 2017): 70-76. https://doi.org/10.36753/mathenot.421702.
EndNote Giri RK, Pradhan S (April 1, 2017) On the Properties of Ascent and Descent of Composition Operator on Orlicz Spaces. Mathematical Sciences and Applications E-Notes 5 1 70–76.
IEEE R. K. Giri and S. Pradhan, “On the Properties of Ascent and Descent of Composition Operator on Orlicz Spaces”, Math. Sci. Appl. E-Notes, vol. 5, no. 1, pp. 70–76, 2017, doi: 10.36753/mathenot.421702.
ISNAD Giri, Ratan Kumar - Pradhan, Shesadev. “On the Properties of Ascent and Descent of Composition Operator on Orlicz Spaces”. Mathematical Sciences and Applications E-Notes 5/1 (April 2017), 70-76. https://doi.org/10.36753/mathenot.421702.
JAMA Giri RK, Pradhan S. On the Properties of Ascent and Descent of Composition Operator on Orlicz Spaces. Math. Sci. Appl. E-Notes. 2017;5:70–76.
MLA Giri, Ratan Kumar and Shesadev Pradhan. “On the Properties of Ascent and Descent of Composition Operator on Orlicz Spaces”. Mathematical Sciences and Applications E-Notes, vol. 5, no. 1, 2017, pp. 70-76, doi:10.36753/mathenot.421702.
Vancouver Giri RK, Pradhan S. On the Properties of Ascent and Descent of Composition Operator on Orlicz Spaces. Math. Sci. Appl. E-Notes. 2017;5(1):70-6.

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