Cartan subalgebras of operator ideals (Q2805997)

The paper under review studies Cartan subalgebras in arbitrary ideals of the algebra of bounded operators on a separable infinite dimensional complex Hilbert space. For each non-zero proper ideal, an uncountable family of pairwise not conjugated Cartan subalgebras of this ideal is constructed. For symmetrically normed ideals which are duals of some Banach space, it is shown that the conjugacy classes of Cartan subalgebras form a smooth manifold endowed with groups of smooth transformations and are equivarinatly diffeomorphic to each other. Finally, the paper constructs the unique diffeomorphism class of full flag manifolds of the group of certain unitary operators.