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arXiv:1307.6118 [math.FA]AbstractReferencesReviewsResources

On extendibility and decomposability of certain *-linear maps into C (X)

Ulrich Haag

Published 2013-07-23Version 1

We consider *-linear maps into a commutative C*-algebra C (X) of continuous functions on a locally compact Hausdorff space X with certain specified properties and prove two results: (1) an extension result for a class of *-linear maps Y --> C (X) which may be called of locally compact type (locally finite) with respect to an inclusion Y < X of normed vector spaces, and (2) a minimal decomposition for certain *-linear maps into C (X) (absolutely continuous) as a difference of two positive maps.

Comments: 8 pages
Categories: math.FA
Subjects: 46L07
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