Renorming AM-spaces

Oikhberg, T.; Tursi, M.

doi:10.1090/proc/15714

Renorming AM-spaces
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by T. Oikhberg and M. A. Tursi PDF

Proc. Amer. Math. Soc. 150 (2022), 1127-1139 Request permission

Abstract:

We prove that any separable AM-space $X$ has an equivalent lattice norm for which no non-trivial surjective lattice isometries exist. Moreover, if $X$ has no more than one atom, then this new norm may be an AM-norm. As our main tool, we introduce and investigate the class of so called regular AM-spaces, which “approximate” general AM-spaces.

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