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Chain rules for canonical state extensions on von Neumann algebras

Carlo Cecchini, Dénes Petz (1993)

Colloquium Mathematicae

In previous papers we introduced and studied the extension of a state defined on a von Neumann subalgebra to the whole of the von Neumann algebra with respect to a given state. This was done by using the standard form of von Neumann algebras. In the case of the existence of a norm one projection from the algebra to the subalgebra preserving the given state our construction is simply equivalent to taking the composition with the norm one projection. In this paper we study couples of von Neumann subalgebras...

Characterizing Fréchet-Schwartz spaces via power bounded operators

Angela A. Albanese, José Bonet, Werner J. Ricker (2014)

Studia Mathematica

We characterize Köthe echelon spaces (and, more generally, those Fréchet spaces with an unconditional basis) which are Schwartz, in terms of the convergence of the Cesàro means of power bounded operators defined on them. This complements similar known characterizations of reflexive and of Fréchet-Montel spaces with a basis. Every strongly convergent sequence of continuous linear operators on a Fréchet-Schwartz space does so in a special way. We single out this type of "rapid convergence" for a sequence...

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