Krein Space Representations and Radon–Nikodým Theorem for Local α-Completely Positive Maps

In this paper, we prove a Krein space J -representation theorem for local α -completely positive maps on locally C ∗ -algebras. Using this representation, we construct a Krein space J -representation associated with a pair of two maps ( φ , Φ ) where φ is a local α -completely positive map on a loca...

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Bibliographic Details
Published in:Complex analysis and operator theory 2021-06, Vol.15 (4), Article 79
Main Authors: Heo, Jaeseong, Ji, Un Cig
Format: Article
Language:English
Subjects:
Analysis
Infinite-dimensional Analysis and Non-commutative Theory
Mathematics
Mathematics and Statistics
Operator Theory
Radon
Representations
Theorems
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Summary:In this paper, we prove a Krein space J -representation theorem for local α -completely positive maps on locally C ∗ -algebras. Using this representation, we construct a Krein space J -representation associated with a pair of two maps ( φ , Φ ) where φ is a local α -completely positive map on a locally C ∗ -algebra and Φ is a φ -map. Also, we discuss the minimality of Krein space J -representations, and as an application, we establish the Radon–Nikodým theorem for local α -completely positive maps.
ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-021-01118-2