A scattered element of a Banach algebra is an element with at most countable spectrum. The set of all scattered elements is denoted by (). The scattered radical is the largest ideal consisting of scattered elements. We characterize in several ways central elements of modulo the scattered radical. As a consequence, it is shown that the following conditions are equivalent: (i) () + () ⊂ (); (ii) ()() ⊂ (); (iii) .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm214-2-6,
author = {Peng Cao},
title = {Scattered elements of Banach algebras},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {195-200},
zbl = {1279.47055},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm214-2-6}
}
Peng Cao. Scattered elements of Banach algebras. Studia Mathematica, Tome 215 (2013) pp. 195-200. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm214-2-6/