Polynomially compact derivations on Banach algebras

Matej Brešar, and Yuri V. Turovskii. "Polynomially compact derivations on Banach algebras." Studia Mathematica 190.2 (2009): 185-191. <http://eudml.org/doc/284471>.

@article{MatejBrešar2009,
abstract = {We consider a continuous derivation D on a Banach algebra 𝓐 such that p(D) is a compact operator for some polynomial p. It is shown that either 𝓐 has a nonzero finite-dimensional ideal not contained in the radical rad(𝓐) of 𝓐 or there exists another polynomial p̃ such that p̃(D) maps 𝓐 into rad(𝓐). A special case where Dⁿ is compact is discussed in greater detail.},
author = {Matej Brešar, Yuri V. Turovskii},
journal = {Studia Mathematica},
keywords = {polynomially compact derivation; power compact derivation; Banach algebra; radical; minimal idempotent},
language = {eng},
number = {2},
pages = {185-191},
title = {Polynomially compact derivations on Banach algebras},
url = {http://eudml.org/doc/284471},
volume = {190},
year = {2009},
}

TY - JOUR
AU - Matej Brešar
AU - Yuri V. Turovskii
TI - Polynomially compact derivations on Banach algebras
JO - Studia Mathematica
PY - 2009
VL - 190
IS - 2
SP - 185
EP - 191
AB - We consider a continuous derivation D on a Banach algebra 𝓐 such that p(D) is a compact operator for some polynomial p. It is shown that either 𝓐 has a nonzero finite-dimensional ideal not contained in the radical rad(𝓐) of 𝓐 or there exists another polynomial p̃ such that p̃(D) maps 𝓐 into rad(𝓐). A special case where Dⁿ is compact is discussed in greater detail.
LA - eng
KW - polynomially compact derivation; power compact derivation; Banach algebra; radical; minimal idempotent
UR - http://eudml.org/doc/284471
ER -