Almost multiplicative functionals
Studia Mathematica, Tome 124 (1997) no. 1, pp. 37-58
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
A linear functional F on a Banach algebra A is almost multiplicative if |F(ab) - F(a)F(b)| ≤ δ∥a∥ · ∥b∥ for a,b ∈ A, for a small constant δ. An algebra is called functionally stable or f-stable if any almost multiplicative functional is close to a multiplicative one. The question whether an algebra is f-stable can be interpreted as a question whether A lacks an almost corona, that is, a set of almost multiplicative functionals far from the set of multiplicative functionals. In this paper we discuss f-stability for general uniform algebras; we prove that any uniform algebra with one generator as well as some algebras of the form R(K), K ⊂ ℂ, and A(Ω), $Ω ⊂ ℂ^{n}$, are f-stable. We show that, for a Blaschke product B, the quotient algebra $H^{∞}/BH^{∞}$ is f-stable if and only if B is a product of finitely many interpolating Blaschke products.
@article{10_4064_sm_124_1_37_58,
author = {Krzysztof Jarosz},
title = {Almost multiplicative functionals},
journal = {Studia Mathematica},
pages = {37--58},
publisher = {mathdoc},
volume = {124},
number = {1},
year = {1997},
doi = {10.4064/sm-124-1-37-58},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-124-1-37-58/}
}
Krzysztof Jarosz. Almost multiplicative functionals. Studia Mathematica, Tome 124 (1997) no. 1, pp. 37-58. doi: 10.4064/sm-124-1-37-58
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