arXiv subjects
Publications and source records attributed to C. Trapani.
In this short note we give some techniques for constructing, starting from a {\it sufficient} family $\mc F$ of semifinite or finite traces on a von Neumann algebra $\M$, a new trace which is faithful.
In this paper the problem of recovering an algebraic dynamics in a perturbative approach is discussed. The mathematical environment in which the physical problem is considered is that of algebras of unbounded operators endowed with the quasi-uniform topology. After some remarks on the domain of the perturbation, conditions are given for the dynamics to exist as the limit of a net of regularized linear maps.
The Banach space $L^p(X,μ)$, for $X$ a compact Hausdorff measure space, is considered as a special kind of quasi *-algebra (called CQ*-algebra) over the C*-algebra $C(X)$ of continuous functions on $X$. It is shown that, for $p \geq 2$, $(L^p(X,μ), C(X))$ is *-semisimple (in a generalized sense). Some consequences of this fact are derived.