0000000001110162
AUTHOR
C. Trapani
The completion of a C*-algebra with a locally convex topology
There are examples of C*-algebras A that accept a locally convex *-topology t coarser than the given one, such that Ae[t] (the completion of A with respect to t) is a GB*-algebra. The multiplication of A[t] may be or not be jointly continuous. In the second case, Ae[t] may fail being a locally convex *-algebra, but it is a partial *-algebra. In both cases the structure and the representation theory of Ae[t] are investigated. If A[t+] denotes the t-closure of the positive cone A+ of the given C*-algebra A, then the property A[t]+ \cap (−A[t]+) = {0} is decisive for the existence of certain faithful *-representations of the corresponding *-algebra Ae[t].
Italian cancer figures, report 2014: Prevalence and cure of cancer in Italy
This Report intends to estimate the total number of people still alive in 2010 after cancer diagnosis in Italy, regardless of the time since diagnosis, and to project these estimates to 2015. This study is also aimed to estimate the number of already cured cancer patients, whose mortality rates have become undistinguishable from that of the general population of the same age and sex.The study took advantage of the information from the AIRTUM database, which included 29 Cancer Registries (covering 21 million people, 35% of the Italian population). A total of 1,624,533 cancer cases diagnosed between 1976 and 2009 contributed to the study. For each registry, the observed prevalence was calcula…
Banach Partial *-Algebras and Quantum Models
C*-algebras are, as known, the basic mathematical ingredient of the Haag- Kastler (Haag and Kastler 1964) algebraic approach to quantum systems, with infinitely many degrees of freedom. The usual procedure starts, in fact, with associating to each bounded region V of the configuration space of the system the C*-algebra AV of local observables in V. The uniform completion A of the algebra generated by the AV ’s is then considered as the C*-algebra of observables of the system
Extension of representations in quasi *-algebras
Let $(A, A_o)$ be a topological quasi *-algebra, which means in particular that $A_o$ is a topological *-algebra, dense in $A$. Let $\pi^o$ be a *-representation of $A_o$ in some pre-Hilbert space ${\cal D} \subset {\cal H}$. Then we present several ways of extending $\pi^o$, by closure, to some larger quasi *-algebra contained in $A$, either by Hilbert space operators, or by sesquilinear forms on ${\cal D}$. Explicit examples are discussed, both abelian and nonabelian, including the CCR algebra.
A Note on the algebraic approach to the «almost» mean-field Heisenberg model
We generalize to an «almost» mean-field Heisenberg model the algebraic approach already formulated for Ising models. We show that there exists a family of «relevant» states on which the algebraic dynamics αt can be defined. © 1993 Società Italiana di Fisica.
Order bounded elements of topological *-algebras
Several different notions of {\em bounded} element of a topological *-algebra $\A$ are considered. The case where boundedness is defined via the natural order of $\A$ is examined in more details and it is proved that under certain circumstances (in particular, when $\A$ possesses sufficiently many *-representations) {\em order boundedness} is equivalent to {\em spectral boundedness}.