Lattice renormings of $C_0(X)$ spaces

期刊论文
发表日期：

2024年9月30日

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T. Oikhberg,
M. A. Tursi

摘要

Suppose X is a locally compact Polish space, and G is a group of lattice isometries of $C_0(X)$ $C_{0} (X)$ which satisfies certain conditions. Then we can equip $C_0(X)$ $C_{0} (X)$ with an equivalent lattice norm $| \! | \! | { \cdot } | \! | \! |$ $| | | \cdot | | |$ so that G is the group of lattice isometries of $(C_0(X), | \! | \! | { \cdot } | \! | \! |)$ $(C_{0} (X), | | | \cdot | | |)$ . As an application, we show that for any locally compact Polish group G there exists a locally compact Polish space X, and a lattice norm $| \! | \! | { \cdot } | \! | \! |$ $| | | \cdot | | |$ on $C_0(X)$ $C_{0} (X)$ , so that G is the group of lattice isometries of $(C_0(X), | \! | \! | { \cdot } | \! | \! |)$ $(C_{0} (X), | | | \cdot | | |)$ .

Lattice renormings of \(C_0(X)\) spaces

摘要