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arXiv · 1003.3123

A description of the logmodular subalgebras in the finite dimensional $C^*$-algebras

Kate Juschenko
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Abstract

We show that every logmodular subalgebra of $M_n(\mathbb{C})$ is unitary equivalent to an algebra of block upper triangular matrices, which was conjectured in \cite{VM}. In particular, this shows that every unital contractive representation of a logmodular subalgebra of $M_n(\mathbb{C})$ is automatically completely contractive.

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Kate Juschenko. 2010-03-16. A description of the logmodular subalgebras in the finite dimensional $C^*$-algebras. https://arxiv.org/abs/1003.3123

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