Narrow Results

For finite dimensional abelian subalgebras of a finite von Neumann algebra, we obtain the value of conditional relative entropy defined by Choda. We also consider the modified invariant defined by Pimsner and Popa.

Let B be a nuclear C*-algebra that has a diagonal subalgebra D in the sense of Kumjian and let A be a closed, not necessarily self-adjoint subalgebra of B that contains D such that A + A* is dense in B. We show that every contractive representation of A has an essentially unique minimal dilation to a C*-representation of B and that the commutant of the representation of A can be lifted to the commutant of the dilation without increasing norms.

Let R be a commutative ring. A not necessarily commutative R-algebra A is called futile if it has only finitely many R-subalgebras. In this paper, we relate the notion of futility to familiar properties of rings and modules. We do this by first reducing to the case where A is commutative. Then we refine the description of commutative futile algebras from Dobbs, Picavet and Picavet-L'Hermite.