Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 1998; 35(1): 237-257

Printed March 1, 1998

Copyright © The Korean Mathematical Society.

The generalized normal state space and unital normal completely positive map

Sa Ge Lee

Seoul National University

Abstract

By introducing the notion of {\it a generalized normal state space}, we give a necessary and sufficient condition for that there exists a unital normal completely positive map from a von Neumann algebra into another, in terms of their generalized normal state spaces.

Keywords: unital normal completely positive map, generalized normal state space, von Neumann algebra, normal $n$-positive linear functional, normal $n$-state, operator affine, hereditary

MSC numbers: 46.L.10

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