This paper characterizes the Banach algebras of continuous functions on which the spectral factorization mapping 𝔖 is continuous or bounded. It is shown that 𝔖 is continuous if and only if the Riesz projection is bounded on the algebra, and that 𝔖 is bounded only if the algebra is isomorphic to the algebra of continuous functions. Consequently, 𝔖 can never be both continuous and bounded, on any algebra under consideration.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-2-4,
author = {Holger Boche and Volker Pohl},
title = {Continuity versus boundedness of the spectral factorization mapping},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {131-145},
zbl = {1161.47011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-2-4}
}
Holger Boche; Volker Pohl. Continuity versus boundedness of the spectral factorization mapping. Studia Mathematica, Tome 187 (2008) pp. 131-145. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-2-4/