Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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MATRIX OPERATORS ON FUNCTION-VALUED FUNCTION SPACES

  • Ong, Sing-Cheong (Department of Mathematics, Central Michigan University) ;
  • Rakbud, Jitti (Department of Mathematics, Faculty of Science Silpakorn University) ;
  • Wootijirattikal, Titarii (Department of Mathematics, Statistics and Computer Faculty of Science, Ubon Ratchathani University)
  • Received : 2018.12.17
  • Accepted : 2019.03.19
  • Published : 2019.06.30
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Abstract

We study spaces of continuous-function-valued functions that have the property that composition with evaluation functionals induce $weak^*$ to norm continuous maps to ${\ell}^p$ space ($p{\in}(1,\;{\infty})$). Versions of $H{\ddot{o}}lder^{\prime}s$ inequality and Riesz representation theorem are proved to hold on these spaces. We prove a version of Dixmier's theorem for spaces of function-valued matrix operators on these spaces, and an analogue of the trace formula for operators on Hilbert spaces. When the function space is taken to be the complex field, the spaces are just the ${\ell}^p$ spaces and the well-known classical theorems follow from our results.

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References

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