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題名: Partially Defined σ -derivations on Semisimple Banach Algebras
作者: Lee, Tsiu-Kwen;Liu, Cheng-Kai
貢獻者: 數學系
日期: 2009-02
上傳時間: 2013-01-07T01:43:40Z
出版者: IMPAN
摘要: 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.
關聯: Studia Mathematica, 190(2): 193-202
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