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alpha-COMPLETELY POSITIVE MAPS ON LOCALLY C*-ALGEBRAS, KREIN MODULES AND RADON-NIKODYM THEOREM

Title
alpha-COMPLETELY POSITIVE MAPS ON LOCALLY C*-ALGEBRAS, KREIN MODULES AND RADON-NIKODYM THEOREM
Author
허재성
Keywords
locally C*-algebra; Hilbert locally C*-module; alpha-completely positive map; J-representation; Krein module; minimal Krein quadruple; non-commutative Radon-Nikodym theorem; STAR-ALGEBRAS; TENSOR-PRODUCTS; HILBERT MODULES; INVERSE LIMITS
Issue Date
2013-01
Publisher
Korean Mathematical SOC
Citation
Journal of the Korean Mathematical Society, 2013, 50(1), P.61-80
Abstract
In this paper, we study alpha-completely positive maps between locally C*-algebras. As a generalization of a completely positive map, an a-completely positive map produces a Krein space with indefinite metric, which is useful for the study of massless or gauge fields. We construct a KSGNS type representation associated to an a-completely positive map of a locally C*-algebra on a Krein locally C*-module. Using this construction, we establish the Radon-Nikodym type theorem for alpha-completely positive maps on locally C*-algebras. As an application, we study an extremal problem in the partially ordered cone of a-completely positive maps on a locally C*-algebra.
URI
http://koreascience.or.kr/article/ArticleFullRecord.jsp?cn=DBSHBB_2013_v50n1_61http://hdl.handle.net/20.500.11754/41441
ISSN
0304-9914
DOI
10.4134/JKMS.2013.50.1.061
Appears in Collections:
COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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