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