허재성
2018-03-01T03:45:19Z
2018-03-01T03:45:19Z
2013-01
Journal of the Korean Mathematical Society, 2013, 50(1), P.61-80
0304-9914
http://koreascience.or.kr/article/ArticleFullRecord.jsp?cn=DBSHBB_2013_v50n1_61
http://hdl.handle.net/20.500.11754/41441
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.
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0005070).This research was supported by Basic Science Research Program through the NRF funded by the MEST (No. R01-2010-002-2514-0).
en
Korean Mathematical SOC
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
alpha-COMPLETELY POSITIVE MAPS ON LOCALLY C*-ALGEBRAS, KREIN MODULES AND RADON-NIKODYM THEOREM
Article
1
50
10.4134/JKMS.2013.50.1.061
61-80
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
Heo, Jaeseong
Ji, Un Cig
Kim, Young Yi
2013005607
S
COLLEGE OF NATURAL SCIENCES[S]
DEPARTMENT OF MATHEMATICS
hjs