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

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

2010-03-16

arxiv.org/abs/1003.3123v1

Mathematics

Operator Algebras

7 pages

Scientific paper

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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