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Please use this identifier to cite or link to this item:
http://ir.ncue.edu.tw/ir/handle/987654321/15012
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| Title: | Partially Defined σ -derivations on Semisimple Banach Algebras |
| Authors: | Lee, Tsiu-Kwen;Liu, Cheng-Kai |
| Contributors: | 數學系 |
| Date: | 2009-02
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| Issue Date: | 2013-01-07T01:43:40Z
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| Publisher: | IMPAN |
| 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. |
| Relation: | Studia Mathematica, 190(2): 193-202 |
| Appears in Collections: | [數學系] 期刊論文
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| 2020101910019.pdf | 80Kb | Adobe PDF | 410 | View/Open |
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