Partially defined σ-derivations on semisimple Banach algebras
Resource
Studia Mathematica,190(2),193-202.
Studia mathematica 190: 193-202
Journal
Studia Mathematica
Pages
193-202
Date Issued
2009
Date
2009
Author(s)
Liu, C. K.
Abstract
Let A be a semisimple Danach 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 Danach algebra with nontrivial idempotents is continuous if it satisfies the σ-derivation expansion formula on zero products. © Instytut Matematyczny PAN, 2009.
Type
journal article
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