Automatic continuity of -derivations on *-algebras
By Madjid Mirzavaziri, Mohammad Sal Moslehian. 2005
95 citations recorded by the source corpus.
Let A be a C�-algebra acting on a Hilbert space H, � : A ! B(H) be a linear mapping and d : A ! B(H) be a �-derivation. Generalizing the celebrated theorem of Sakai, we prove that ifis a continuous �-mapping then d is automatically continuous. In addition, we show the converse is true in the sense that if d is a continuous �-�-derivation then there exists a continuous linear mapping � : A ! B(H) such that d is �-�-derivation. The continuity of the so-called �-(�,�)-derivations is also discussed.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/0c93439da1f8e91917cc95cf5f71d6486877d64f
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Characterization of Higher Derivations on Algebras (2010, background): “In particular, an automatic continuity problem for -derivations is considered in [9], and an achievement of continuity of -derivations without linearity is given in [6].”