Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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WEIGHTED COMPOSITION OPERATORS ON NACHBIN SPACES WITH OPERATOR-VALUED WEIGHTS

  • Klilou, Mohammed (Department of Mathematics Team GrAAF, Laboratory LMSA, Center CeReMAR Faculty of Sciences, Mohammed V University in Rabat) ;
  • Oubbi, Lahbib (Department of Mathematics Team GrAAF, Laboratory LMSA, Center CeReMAR Ecole Normale Superieure, Mohammed V University in Rabat)
  • Received : 2017.03.09
  • Accepted : 2018.03.09
  • Published : 2018.10.31
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Abstract

Let A be a normed space, ${\mathcal{B}}(A)$ the algebra of all bounded operators on A, and V a family of strongly upper semicontinuous functions from a Hausdorff completely regular space X into ${\mathcal{B}}(A)$. In this paper, we investigate some properties of the weighted spaces CV (X, A) of all A-valued continuous functions f on X such that the mapping $x{\mapsto}v(x)(f(x))$ is bounded on X, for every $v{\in}V$, endowed with the topology generated by the seminorms ${\parallel}f{\parallel}v={\sup}\{{\parallel}v(x)(f(x)){\parallel},\;x{\in}X\}$. Our main purpose is to characterize continuous, bounded, and locally equicontinuous weighted composition operators between such spaces.

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References

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