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A Radon–Nikodým theorem for completely positive invariantmultilinear maps and its applications

Published online by Cambridge University Press:  01 February 2002

JAESEONG HEO
JAESEONG HEO
Affiliation:
Department of Mathematics, Chungnam National University, Taejon 305-764, Korea. e-mail: [email protected]
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Abstract

Noncommutative Radon–Nikodým theorems have attracted a great deal of attention in the theory of operator algebras. There has been considerable work on non-commutative Radon–Nikodým theorems not only for C*-algebras but also for algebras of unbounded operators [3, 5, 8, 9, 12, 13]. In this paper, we will develop a Radon–Nikodým type theorem for completely bounded and completely positive invariant multilinear maps.

The concept of matricial order has turned out to be very important to understand the infinite-dimensional non-commutative structure of operator algebras. As the natural ordering attached to this structure, completely positive maps and completely bounded maps have been studied extensively. Results concerning completely bounded maps have many applications: cohomology of operator algebras, multipliers on group algebras, dilation theory, similarity theory, free product representations, and abstract characterizations of operator algebras.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 132 , Issue 1 , January 2002 , pp. 181 - 192
Copyright
2002 Cambridge Philosophical Society

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