Suppose X is a locally compact Polish space, and G is a group of lattice isometries of C₀(X) which satisfies certain conditions. Then we can equip C₀(X) with an equivalent lattice norm | \! | \! | · | \! | \! | so that G is the group of lattice isometries of (C₀(X), | \! | \! | · | \! | \! |). 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 | \! | \! | · | \! | \! | on C₀(X), so that G is the group of lattice isometries of (C₀(X), | \! | \! | · | \! | \! |).
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Oikhberg et al. (2024) studied this question.
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