Finite Section Method for a Banach Algebra of Convolution Type Operators on $L^p(mathbb{R})$ with Symbols Generated by $PC$ and $SO$. (arXiv:0909.3821v1 [math.FA])

We prove the applicability of the finite section method to an arbitrary
operator in the Banach algebra generated by the operators of multiplication by
piecewise continuous functions and the convolution operators with symbols in
the algebra generated by piecewise continuous and slowly oscillating Fourier
multipliers on $L^p(mathbb{R})$, $1<p<infty$.

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Original source : http://arxiv.org/abs/0909.3821...