An algebra 𝓐 of real- or complex-valued functions defined on a set T shall be called homotonic if 𝓐 is closed under taking absolute values, and for all f and g in 𝓐, the product f × g satisfies |f × g| ≤ |f| × |g|. Our main purpose in this paper is two-fold: to show that the above definition is equivalent to an earlier definition of homotonicity, and to provide a simple inequality which characterizes submultiplicativity and strong stability for weighted sup norms on homotonic algebras.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm195-3-7,
author = {Michael Cwikel and Moshe Goldberg},
title = {Homotonic algebras},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {287-295},
zbl = {1186.46052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm195-3-7}
}
Michael Cwikel; Moshe Goldberg. Homotonic algebras. Studia Mathematica, Tome 192 (2009) pp. 287-295. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm195-3-7/