OPERATOR-VALUED MULTIPLICATION OPERATORS
ON WEIGHTED BANACH FUNCTION SPACES
Ajay Kumar Sharma
Department of Mathematics,
Government Degree College,
Udhampur-182101, Jammu and Kashmir, India

Abstract

In this paper, we study multiplication operators induced by strongly measurable operatorvalued maps on weighted Banach function spaces. We characterize the boundedness, invertibility, closed range, and compactness of such multiplication operators. We also investigate the Fredholm properties of these operators. The results are established in the general setting of vector-valued weighted Banach function spaces with absolutely continuous norms.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 30
Issue: 6
Year: 2017

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References

  1. [1] S. C. Arora, G. Datt, and S. Verma, Multiplication and composition operators on LorentzBochner spaces, Osaka Journal of Math. 44 (2008), No. 4, 629-641.
  2. [2] C. Bennett and R. Sharpley, Interpolation of operators, Pure and Applied Mathematics 129, Academic Press, London, 1988.
  3. [3] D. E. Edmunds and W. D. Evans, Hardy operators, function spaces and embeddings, Springer Berlin, 2004.
  4. [4] Shally Gupta and B. S. Komal, Multiplication operators between Orlicz spaces, Integral Equations and Operator Theory 41 (2001), 324-330.
  5. [5] H. Hudzik, R. Kumar and R. Kumar, Matrix multiplication operators on Banach function spaces, Proc. Indian Acad. Sci. Math. Sci. 116 (2006), No. 1, 71-81.
  6. [6] S. G. Krein, Ju. I. Petunin and E. M. Semenov, Interpolation of linear operators, AMS Translation of Math. Monographs 54, Providence, RI, 1982.
  7. [7] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces II, Function Spaces, Vol. 97, Springer-Verlag, Berlin-New York, 1979.
  8. [8] L. Maligranda, Orlicz Spaces and Interpolation, Seminars in Math. 5, Univ. Estadual de Campinas, Campinas SP, Brazil, 1989.
  9. [9] R. K. Singh and J. S. Manhas, Composition operators on function spaces, North Holland Math. Studies 179, Amsterdam, 1993.
  10. [10] R. K. Singh and N. S. Dharmadhikari, Compact and Fredholm composite multiplication operators, Acta Sci. Math. 52 (1988), no. 3-4, 437-441.