Let Ω a bounded regular1 domain of R and let us denote respectively by | · | and (·, ·) the natural norm and inner product of the space H = L2(Ω). Let V →֒ H be a real Hilbert space that is continuously and densely embedded into H. Denote by ‖ · ‖ and < ·, · >V respectively the norm and the inner product of V and by L ∈ L(V, V ) the unique linear continuous operator from V to V , the dual of V ,...

we prove that each normal automorphism of the $n$-periodic product of cyclic groups of odd order $rge1003$ is inner, whenever $r$ divides $n$.

We summarize the basic properties of continuous tensor product systems of Hilbert spaces and their role in non-commutative dynamics. These are lecture notes, not intended for publication. 1. Concrete Product Systems In these notes we assume the reader is familiar with the definition and basic properties of E0-semigroups, and has some familiarity with their role in noncommutative dynamics. Our p...

The information metric arises in statistics as a natural inner product on a space of probability distributions. In general this inner product is positive semi-definite but is potentially degenerate. By associating to an instanton its energy density, we can examine the information metric g on the moduli spaces M of self-dual connections over Riemannian 4-manifolds. Compared with the more widely ...

The state space of a finite quantum system is identified with the set of positive semidefinite matrices of trace 1. The set of all strictly positive definite matrices of trace 1 becomes naturally a differentiable manifold and the Bogoliubov–Kubo– Mori scalar product defines a Riemannian structure on it. Reference 4 tells about the relation of this metric to the von Neumann entropy functional. I...