Multiplication and Composition operators on ωp (f)
DOI:
https://doi.org/10.4067/S0716-09172013000400002Keywords:
Modulus function, Multiplication operator, Composition operator, Closed range, invertibility.Abstract
In this paper we characterize the boundedness, closed range, in-vertibility of the multiplication operators acting on sequence spaces wp(f) defined by a modulus function. We also make an efforts to study some properties of composition operators on these spaces.References
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[8] Kuldip Raj, B. S. Komal and Vinay Khosla, Composition operators on sequence spaces of entire functions. Int. Electron. J. Pure Appl. Math., 1 : pp. 469-474, (2010).
[9] E. Savas, On some generalized sequence spaces defined by a modulus. Indian J. pure Appl. Math., 30 : pp. 459-464, (1999).
[10] R. K. Singh and J. S. Manhas, Composition operators on function spaces. North-Holland, (1993).
[11] H. Takagi and K. Yokouchi, Multiplication and composition operators between Lp-spaces. Contemp. Math., 232 : pp. 321-338, (1999).
[2] T. Bilgen, On statistical convergence. An. Univ. Timisoara Ser. Math. Inform., 32 : pp. 3-7, (1994).
[3] M. A. Khan, Some sequence spaces with an index defined by a modulus function. Thai J. Math., 2 : 259-264, (2004).
[4] B. S. Komal and Kuldip Raj, Multiplication operators induced by operator valued maps. Int. J. Contemp. Math. Sci., Vol.3 : pp. 667- 673, (2008).
[5] B. S. Komal and P. S. Singh, Composition operators on the space of entire functions. Kodai Math. J., 14 : pp. 463-469, (1991).
[6] G. G. Lorentz, A contribution to the theory of divergent series. Acta. Math., 80 : pp. 167-190, (1948).
[7] E. Malkowsky and E. Savas, Some ë-sequence spaces defined by a modulus. Arch. Math., 36 : pp. 219-228, (2000).
[8] Kuldip Raj, B. S. Komal and Vinay Khosla, Composition operators on sequence spaces of entire functions. Int. Electron. J. Pure Appl. Math., 1 : pp. 469-474, (2010).
[9] E. Savas, On some generalized sequence spaces defined by a modulus. Indian J. pure Appl. Math., 30 : pp. 459-464, (1999).
[10] R. K. Singh and J. S. Manhas, Composition operators on function spaces. North-Holland, (1993).
[11] H. Takagi and K. Yokouchi, Multiplication and composition operators between Lp-spaces. Contemp. Math., 232 : pp. 321-338, (1999).
How to Cite
[1]
K. Raj, S. K. Sharma, and S. Jamwal, “Multiplication and Composition operators on ωp (f)”, Proyecciones (Antofagasta, On line), vol. 32, no. 4, pp. 321-332, 1.
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