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

2013/07/23 by Ulrich Haag, Haag, Ulrich
Mathematics · #46L07 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46L07

paper · pdf · doi:10.48550/arxiv.1307.6118

8 pages

arxiv created 2013/07/23 · arxiv updated 2013/07/24

Abstract

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.

Related

• Automatic continuity and C₀(Ω)-linearity of linear maps between C₀(Ω)-modules
• Separably injective C*-algebras
• On isomorphisms of algebras of compactly supported continuous functions
• Compact failure of multiplicativity for linear maps between Banach algebras
• An Algebraic and Logical approach to continuous images