Year: 2026
Type: article
Abstract: We characterize all $$f\!$$ f -algebra products on AM-spaces by constructing a canonical AM-space $$W_X$$ W X associated to each AM-space X , such that the $$f\!$$ f -algebra products on X correspond bijectively to the positive cone $$(W_X)_+$$ ( W X ) + . This generalizes the classical description of $$f\!$$ 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: Mathematische Zeitschrift
Author: David Muñoz-Lahoz
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W7160698285