Partially defined σ-derivations on semisimple Banach algebras

Tsiu-Kwen Lee, and Cheng-Kai Liu. "Partially defined σ-derivations on semisimple Banach algebras." Studia Mathematica 190.2 (2009): 193-202. <http://eudml.org/doc/286557>.

@article{Tsiu2009,
abstract = {Let A be a semisimple Banach algebra with a linear automorphism σ and let δ: I → A be a σ-derivation, where I is an ideal of A. Then Φ(δ)(I ∩ σ(I)) = 0, where Φ(δ) is the separating space of δ. As a consequence, if I is an essential ideal then the σ-derivation δ is closable. In a prime C*-algebra, we show that every σ-derivation defined on a nonzero ideal is continuous. Finally, any linear map on a prime semisimple Banach algebra with nontrivial idempotents is continuous if it satisfies the σ-derivation expansion formula on zero products.},
author = {Tsiu-Kwen Lee, Cheng-Kai Liu},
journal = {Studia Mathematica},
keywords = {Banach algebra; prime -algebra; -derivation; closability; continuity},
language = {eng},
number = {2},
pages = {193-202},
title = {Partially defined σ-derivations on semisimple Banach algebras},
url = {http://eudml.org/doc/286557},
volume = {190},
year = {2009},
}

TY - JOUR
AU - Tsiu-Kwen Lee
AU - Cheng-Kai Liu
TI - Partially defined σ-derivations on semisimple Banach algebras
JO - Studia Mathematica
PY - 2009
VL - 190
IS - 2
SP - 193
EP - 202
AB - Let A be a semisimple Banach algebra with a linear automorphism σ and let δ: I → A be a σ-derivation, where I is an ideal of A. Then Φ(δ)(I ∩ σ(I)) = 0, where Φ(δ) is the separating space of δ. As a consequence, if I is an essential ideal then the σ-derivation δ is closable. In a prime C*-algebra, we show that every σ-derivation defined on a nonzero ideal is continuous. Finally, any linear map on a prime semisimple Banach algebra with nontrivial idempotents is continuous if it satisfies the σ-derivation expansion formula on zero products.
LA - eng
KW - Banach algebra; prime -algebra; -derivation; closability; continuity
UR - http://eudml.org/doc/286557
ER -