A Theory of Dimension
funct-an
2008-02-03 v1 Operator Algebras
Abstract
In which a theory of dimension related to the Jones index and based on the notion of conjugation is developed. An elementary proof of the additivity and multiplicativity of the dimension is given and there is an associated trace. Applications are given to a class of endomorphisms of factors and to the theory of subfactors. An important role is played by a notion of amenability inspired by the work of Popa.
Keywords
Cite
@article{arxiv.funct-an/9604008,
title = {A Theory of Dimension},
author = {Roberto Longo and John E. Roberts},
journal= {arXiv preprint arXiv:funct-an/9604008},
year = {2008}
}
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