  We introduce and study the notion of maximal tracial algebras. We prove
several results in a general setting based on dual pairs and multiplier pairs.
In a special case that X is a Banach space we determine the abelian subalgebras
of B(X) that are maximal tracial for rank-one tensors. We also make slight
connections between our ideas and the Kadison Similarity Problem and also the
Connes' Embedding Problem.
