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Download (), Marina HARALAMPIDOU Department of Mathematics, University of Athens
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Transcript
Marina HARALAMPIDOU ([email protected]), Department of Mathematics, University of Athens Panepistimioupolis, GR-157 84, Athens, Greece, The Krull nature of locally C ∗ -algebras. ABSTRACT. Any complete locally m-convex algebra, whose normed factors in its Arens-Michael decomposition are Krull algebras is also Krull. In particular, any locally C ∗ -algebra is Krull. Considering perfect projective systems, we give another proof of the fact that any Fréchet locally C ∗ -algebra is Krull. Furthermore, a unital proper complete locally m-convex H ∗ -algebra with continuous involution is a locally C ∗ algebra and hence Krull. The class of Krull (topological) algebras is closed with respect to cartesian products, topological algebra isomorphic images, and perfect projective limits.
