Partially defined σ-derivations on semisimple Banach algebras

• Autorzy: Tsiu-Kwen Lee , Cheng-Kai Liu
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46H15: Representations of topological algebras
• 46H40: Automatic continuity
• 47B47: Commutators, derivations, elementary operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 190
• Numer: 2
• Strony: 193-202

Daty

wydano

2009

Twórcy

autor

Tsiu-Kwen Lee

• Department of Mathematics, National Taiwan University, Taipei 106, Taiwan

autor

Cheng-Kai Liu

• Department of Mathematics, National Changhua University of Education, Changhua 500, Taiwan

Identyfikatory

DOI

10.4064/sm190-2-7