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Inner Derivations on σ‐ C *‐Algebras
Author(s) -
Christopher Phillips N.
Publication year - 1995
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19951760117
Subject(s) - mathematics , quotient , separable space , derivation , pure mathematics , algebra over a field , property (philosophy) , mathematical analysis , medicine , philosophy , surgery , epistemology , artery
We prove the following two improvements of a result of Becker. (1) If A is a pro‐ C *‐algebra, then every derivation on A is approximately inner. (2) If A is a separable σ‐ C *‐algebra, and if every C * quotient of A has the property that every derivation on it is inner, then also every derivation on A is inner. We also give an example of a derivation on a separable σ‐ C *‐algebra which is not inner but which induces an inner derivation on every C * quotient.