Let A be a Banach *-algebra with an identity, continuous involution, center Z and set of self-adjoint elements Σ. Let h ∈ Σ. The set of v ∈ Σ such that (h + iv)ⁿ is normal for no positive integer n is dense in Σ if and only if h ∉ Z. The case where A has no identity is also treated.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-3-1,
author = {B. Yood},
title = {Non-normal elements in Banach *-algebras},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {201-204},
zbl = {1062.46042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-3-1}
}
B. Yood. Non-normal elements in Banach *-algebras. Studia Mathematica, Tome 162 (2004) pp. 201-204. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-3-1/