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Partially defined σ-derivations on semisimple Banach algebras

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Lee T.-K., Liu C.-K.

Studia Mathematica

2009

tom 190

nr 2

193-202

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.

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1 Studia Mathematica

1 Lee T.-K.

1 Liu C.-K.

1 2009

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Partially defined σ-derivations on semisimple Banach algebras