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

Yıl 2017, Cilt: 5 Sayı: 1, 70 - 76, 30.04.2017

Ratan Kumar Giri Shesadev Pradhan

https://doi.org/10.36753/mathenot.421702

Öz

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

Anahtar Kelimeler

Orlicz function, Orlicz Space, Radon-Nikodym derivative, Composition operator

Kaynakça

• [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.