Year: 2025
Type: preprint
Abstract: We characterize all $f$-algebra products on AM-spaces by constructing a canonical AM-space $W_X$ associated to each AM-space $X$, such that the $f$-algebra products on $X$ correspond bijectively to the positive cone $(W_X)_+$. This generalizes the classical description of $f$-algebra products on $C(K)$ spaces. We also identify the unique product (when it exists) that embeds $X$ as a closed subalgebra of $C(K)$, and study AM-spaces for which this product exists -- the so-called AM-algebras. Finally, we investigate AM-spaces that admit only the zero product, providing a characterization in the AL-space case and examples showing that no simple characterization exists in general.
Source: arXiv (Cornell University)
Author: Muñoz-Lahoz, David
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979299408
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