Calkin images of Fourier convolution operators with slowly oscillating symbols

2020/08/04 by Fernandes, Cláudio A., Karlovich, Alexei Yu., Karlovich, Yuri I. · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2008.02634

Abstract

Let Φ be a C^*-subalgebra of L^∞(ℝ) and SO_X(ℝ)^\diamond be the Banach algebra of slowly oscillating Fourier multipliers on a Banach function space X(ℝ). We show that the intersection of the Calkin image of the algebra generated by the operators of multiplication aI by functions a∈Φ and the Calkin image of the algebra generated by the Fourier convolution operators W⁰(b) with symbols in SO_X(ℝ)^\diamond coincides with the Calkin image of the algebra generated by the operators of multiplication by constants.

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