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

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Published: Jun 30, 2019
Keywords:
$C^*$-algebra, function space, operators, $M$-ideal, dual space
Mathematics Subject Classification:
46E40

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Sing-Cheong Ong
Department of Mathematics, Central Michigan University Mount Pleasant, MI 48859, USA
Jitti Rakbud
Department of Mathematics, Faculty of Science Silpakorn University, Nakorn Pathom, 73000, Thailand
Titarii Wootijirattikal
Department of Mathematics, Statistics and Computer Faculty of Science, Ubon Ratchathani University Ubon Ratchathani 34190, Thailand

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 $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.


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Supporting Agencies

Thailand Research Fund

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