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Lattice renormings of $C_0(X)$ spaces
- Publication Year :
- 2024
-
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 $(C_0(X), | \! | \! | \cdot | \! | \! |)$.
- Subjects :
- Mathematics - Functional Analysis
46B03, 46B04, 46B42, 46E05
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2405.11148
- Document Type :
- Working Paper