Composition Operators on Lorentz-Karamata-Bochner Spaces

ANURADHA GUPTA¹ and NEHA BHATIA^2,

¹Department of Mathematics, Delhi College of Arts and Commerce, University of Delhi, Delhi-110023, India

²Department of Mathematics, University of Delhi, Delhi -110007, India

Cite this paper:
ANURADHA GUPTA and NEHA BHATIA. Composition Operators on Lorentz-Karamata-Bochner Spaces. American Journal of Mathematical Analysis. 2015; 3(1):21-25. doi: 10.12691/ajma-3-1-5

Abstract

In this paper, study of the composition operators on Lorentz-Karamata-Bochner spaces and characterization of the properties like boundedness, closedness and essential range of these operators on the space has been made.

Keywords:
slowly varying function Lorentz-Karamata-Bochner spaces composition operators closed range essential range

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References:

[1]	S.C. Arora, G. Datt and S. Verma, Multiplication and composition operators on Lorentz-Bochner spaces, Osaka J. Math. 45 (2008), 629-641.
[2]	S.C Arora, G. Datt and S. Verma, Multiplication operators on Lorentz spaces, Indian J. Math. 48 (2006), 317-329.
[3]	P. Bala, A. Gupta, N. Bhatia, Multiplication operators on Orlicz-Lorentz sequence spaces, Int. Journal of Math. Analysis 7 (2013), no. 30, 1461-1469.
[4]	D.E. Edmunds and W.D. Evans, Hardy operators, function spaces and embeddings, Springer Monographs in Mathematics Springer-Verlag, Belin, 2004.
[5]	I. Eryilmaz, Multiplication operators on Lorentz-Karamata-Bochner spaces, Math. Slovaca 62 (2012), no. 2, 293-300.
[6]	B.S. Komal and S. Gupta, Multiplication operators between Orlicz spaces, Integral Equations Operator Theory 41 (2001), 324-330.
[7]	V.N. Mishra, Some problems on Approximations of Functions in Banach spaces, PhD Thesis (2007) Indian Institiute of Technology, Roorkee-247 667, Uttarakhand, India.
[8]	V. N. Mishra, K. Khatri, L. N. Mishra, and Deepmala, Inverse result in simultaneous approximation by Baskakov-Durrmeyer-Stancu operators, Journal of Inequalities and Applications 2013, 2013: 586.
[9]	V. N. Mishra and L. N. Mishra, “Trigonometric Approximation of Signals (Functions) in Lp (p≥1)-Norm,” International Journal of Contemporary Mathematical Sciences, Vol. 7, No. 19, 2012, pp. 909-918.
[10]	E.Seneta, Regularly Varying Functions, Lecture Notes in Math. 508, Springer-Verlag, Berlin, 1976.
[11]	R.K. Singh and J.S. Manhas. Composition operators on function spaces, North Holland Math. Studies 179, North Holland, Amsterdam, 1993.
[12]	H. Takagi and K. Yokouchi, Multiplication and composition operators between two Lp-spaces, In: Function Spaces (Edwardsville, IL, 1998). Contemp. Math. 232, Amer. Math. Soc., Providence, RI, 1999, pp. 321-338.