A few remarks on intermediate subalgebras of an inclusion of C∗-algebras

In this paper, we show that the angle between intermediate [Formula: see text]-subalgebras of an inclusion of simple [Formula: see text]-algebras with finite Watatani index is stable. The notion of angle is instrumental in providing a bound for the cardinality of the lattice of intermediate subalgebras for an irreducible inclusion of simple [Formula: see text]-algebras with finite Watatani index. We improve the existing upper bound for the cardinality of this set.