Scattered elements of Banach algebras

Peng Cao. "Scattered elements of Banach algebras." Studia Mathematica 214.2 (2013): 195-200. <http://eudml.org/doc/286420>.

@article{PengCao2013,
abstract = {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 $_\{sc\}()$ 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) $[(),] ⊂ _\{sc\}()$.},
author = {Peng Cao},
journal = {Studia Mathematica},
keywords = {Jacobson radical; scattered radical; scattered element},
language = {eng},
number = {2},
pages = {195-200},
title = {Scattered elements of Banach algebras},
url = {http://eudml.org/doc/286420},
volume = {214},
year = {2013},
}

TY - JOUR
AU - Peng Cao
TI - Scattered elements of Banach algebras
JO - Studia Mathematica
PY - 2013
VL - 214
IS - 2
SP - 195
EP - 200
AB - 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 $_{sc}()$ 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) $[(),] ⊂ _{sc}()$.
LA - eng
KW - Jacobson radical; scattered radical; scattered element
UR - http://eudml.org/doc/286420
ER -