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arXiv · 0911.0831

Convolution operators on Banach lattices with shift-invariant norms

Nazar Miheisi
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Abstract

Let G be a locally compact abelian group and let μbe a complex valued regular Borel measure on G. In this paper we consider a generalisation of a class of Banach lattices introduced in [6]. We use Laplace transform methods to show that the norm of a convolution operator with symbol μon such a space is bounded below by the L_\infty norm of the Fourier-Stieltjes transform of μ. We also show that for any Banach lattice of locally integrable functions on G with a shift-invariant norm, the norm of a convolution operator with symbol μis bounded above by the total variation of μ.

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Nazar Miheisi. 2009-11-04. Convolution operators on Banach lattices with shift-invariant norms. https://arxiv.org/abs/0911.0831

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