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arXiv · 2405.11148

Lattice renormings of $C_0(X)$ spaces

Timur Oikhberg·Mary Angelica Tursi
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Abstract

Suppose $X$ is a locally compact Polish space, and $G$ is a group of lattice isometries of $C_0(X)$ which satisfies certain conditions. Then we can equip $C_0(X)$ with an equivalent lattice norm $| \! | \! | \cdot | \! | \! |$ so that $G$ is the group of lattice isometries of $(C_0(X), | \! | \! | \cdot | \! | \! |)$. As an application, we show that for any locally compact Polish group $G$ there exists a locally compact Polish space $X$, and an lattice norm $| \! | \! | \cdot | \! | \! |$ on $C_0(X)$, so that $G$ is the group of lattice isometries of $(C_0(X), | \! | \! | \cdot | \! | \! |)$.

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Timur Oikhberg, Mary Angelica Tursi. 2024-05-18. Lattice renormings of $C_0(X)$ spaces. https://arxiv.org/abs/2405.11148

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