Let 𝒜 be a Banach algebra over ℂ with unit 1 and 𝑓: ℂ → ℂ an entire function. Let 𝐟: 𝒜 → 𝒜 be defined by 𝐟(a) = 𝑓(a) (a ∈ 𝒜), where 𝑓(a) is given by the usual analytic calculus. The connections between the periods of 𝑓 and the periods of 𝐟 are settled by a theorem of E. Vesentini. We give a new proof of this theorem and investigate further properties of periods of 𝐟, for example in C*-algebras.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm162-2-6,
author = {Gerd Herzog and Christoph Schmoeger},
title = {On a theorem of Vesentini},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {183-193},
zbl = {1060.46034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm162-2-6}
}
Gerd Herzog; Christoph Schmoeger. On a theorem of Vesentini. Studia Mathematica, Tome 162 (2004) pp. 183-193. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm162-2-6/