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Mathematics > Functional Analysis

arXiv:1409.3377 (math)
[Submitted on 11 Sep 2014]

Title:Extensions of positive operators and functionals

Authors:Zoltán Sebestyén, Zsolt Szűcs, Zsigmond Tarcsay
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Abstract:We consider linear operators defined on a subspace of a complex Banach space into its topological antidual acting positively in a natural sense. The goal of this paper is to investigate of this kind of operators. The main theorem is a constructive characterization of the bounded positive extendibility of these linear mappings. From this result we can characterize the compactness of the extended operators and that when the positive extensions have closed ranges. As a main application of our general extension theorem, we present some necessary and sufficient conditions that a positive functional defined on a left ideal of a Banach $^*$-algebra admits a representable positive extension. The approach we use here is completely constructive.
Subjects: Functional Analysis (math.FA)
MSC classes: 47B25, 47B65
Cite as: arXiv:1409.3377 [math.FA]
  (or arXiv:1409.3377v1 [math.FA] for this version)
  https://doi.org/10.48550/arXiv.1409.3377

Submission history

From: Zsigmond Tarcsay [view email]
[v1] Thu, 11 Sep 2014 10:42:30 UTC (19 KB)
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