Quasinilpotent operators in operator Lie algebras II

Peng Cao. "Quasinilpotent operators in operator Lie algebras II." Studia Mathematica 195.2 (2009): 193-200. <http://eudml.org/doc/285317>.

@article{PengCao2009,
abstract = {In this paper, it is proved that the Banach algebra $\overline\{(ℒ)\}$, generated by a Lie algebra ℒ of operators, consists of quasinilpotent operators if ℒ consists of quasinilpotent operators and $\overline\{(ℒ)\}$ consists of polynomially compact operators. It is also proved that $\overline\{(ℒ)\}$ consists of quasinilpotent operators if ℒ is an essentially nilpotent Engel Lie algebra generated by quasinilpotent operators. Finally, Banach algebras generated by essentially nilpotent Lie algebras are shown to be compactly quasinilpotent.},
author = {Peng Cao},
journal = {Studia Mathematica},
keywords = {essentially nilpotent Lie algebra; quasinilpotent operator; compactly quasinilpotent algebra},
language = {eng},
number = {2},
pages = {193-200},
title = {Quasinilpotent operators in operator Lie algebras II},
url = {http://eudml.org/doc/285317},
volume = {195},
year = {2009},
}

TY - JOUR
AU - Peng Cao
TI - Quasinilpotent operators in operator Lie algebras II
JO - Studia Mathematica
PY - 2009
VL - 195
IS - 2
SP - 193
EP - 200
AB - In this paper, it is proved that the Banach algebra $\overline{(ℒ)}$, generated by a Lie algebra ℒ of operators, consists of quasinilpotent operators if ℒ consists of quasinilpotent operators and $\overline{(ℒ)}$ consists of polynomially compact operators. It is also proved that $\overline{(ℒ)}$ consists of quasinilpotent operators if ℒ is an essentially nilpotent Engel Lie algebra generated by quasinilpotent operators. Finally, Banach algebras generated by essentially nilpotent Lie algebras are shown to be compactly quasinilpotent.
LA - eng
KW - essentially nilpotent Lie algebra; quasinilpotent operator; compactly quasinilpotent algebra
UR - http://eudml.org/doc/285317
ER -