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arXiv · 2008.02634

Calkin images of Fourier convolution operators with slowly oscillating symbols

Cláudio A. Fernandes·Alexei Yu. Karlovich·Yuri I. Karlovich
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Abstract

Let $\Phi$ be a $C^*$-subalgebra of $L^\infty(\mathbb{R})$ and $SO_{X(\mathbb{R})}^\diamond$ be the Banach algebra of slowly oscillating Fourier multipliers on a Banach function space $X(\mathbb{R})$. We show that the intersection of the Calkin image of the algebra generated by the operators of multiplication $aI$ by functions $a\in\Phi$ and the Calkin image of the algebra generated by the Fourier convolution operators $W^0(b)$ with symbols in $SO_{X(\mathbb{R})}^\diamond$ coincides with the Calkin image of the algebra generated by the operators of multiplication by constants.

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Cláudio A. Fernandes, Alexei Yu. Karlovich, Yuri I. Karlovich. 2020-08-04. Calkin images of Fourier convolution operators with slowly oscillating symbols. https://arxiv.org/abs/2008.02634

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