Korean J. Math. Vol. 27 No. 2 (2019) pp.375-415
DOI: https://doi.org/10.11568/kjm.2019.27.2.375

Matrix operators on function-valued function spaces

Main Article Content

Sing-Cheong Ong
Jitti Rakbud
Titarii Wootijirattikal


We study spaces of continuous-function-valued functions that have the property that composition with evaluation functionals induce weak$^{^*}$ to norm continuous maps to $l^p $ space $ (p\in (1, \infty))$. Versions of H\"older'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 $l^p$ spaces and the well-known classical theorems follow from our results.

Article Details

Supporting Agencies

Thailand Research Fund


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