The interplay between representable functionals and derivations on Banach quasi *-algebras

This note aims to highlight the link between representable functionals and derivations on a Banach quasi *-algebra, i.e. a mathematical structure that can be seen as the completion of a normed *-algebra in the case the multiplication is only separately continuous. Representable functionals and derivations have been investigated in previous papers for their importance concerning the study of the structure properties of a Banach quasi *-algebra and applications to quantum models.Comment: Contribution Proceedings of International Conference on Topological Algebras and Applications 201

Representable and continuous functionals on Banach quasi *-algebras

In the study of locally convex quasi *-algebras an important role is played by representable linear functionals; i.e., functionals which allow a GNS-construction. This paper is mainly devoted to the study of the continuity of representable functionals in Banach and Hilbert quasi *-algebras. Some other concepts related to representable functionals (full-representability, *-semisimplicity, etc) are revisited in these special cases. In particular, in the case of Hilbert quasi *-algebras, which are shown to be fully representable, the existence of a 1-1 correspondence between positive, bounded elements (defined in an appropriate way) and continuous representable functionals is proved

Non Destructive Surface and Sub-surface Material Analysis using Scanning SQUID Magnetic Microscope

Non Destructive Testing (NDT) based on magnetic technique for the investigation of surface and sub-surface material properties is carried out using a room-temperature sample Scanning Magnetic Microscope. The performances of such instrument are well suited in the field of non destructive evaluation, thanks to the good combination of the spatial resolution and the magnetic field sensitivity of its own superconducting magnetic sensor. The aim of this work is to show the capability and the advantages of the NDT technique based on Superconducting Quantum Interference Device (SQUID) sensors. We start by describing our Scanning SQUID Microscope in terms of its performances, the different non destructive techniques we can apply to perform the measurements, and the efforts we have done to improve its capability to detect weak magnetic field variations. Two main applications are presented. On of this is based on the high magnetic field sensitivity of the SQUID sensor at low frequencies, and it consists to excite the sample with an alternating magnetic field (AC). This technique is applied to detect subsurface flaws in paramagnetic samples, for instance, in multilayer structures of aeronautical interest. The other field of application concerns the capability of the sensor to detect, with high spatial resolution, the direct magnetic field (DC) distribution on ferromagnetic samples, due to their residual magnetization. In this way, we can visualize magnetic domain structures of ferromagnetic particles. This capability is also exploited to evaluate the changing of magnetic field distribution in proximity of crack initialization on structural steels, subjected to fatigue cycles

Fixed point and homotopy results for mixed multi-valued mappings in 0-complete partial metric spaces

We give sufficient conditions for the existence of common fixed points for a pair of mixed multi-valued mappings in the setting of 0-complete partial metric spaces. An example is given to demonstrate the usefulness of our results over the existing results in metric spaces. Finally, we prove a homotopy theorem via fixed point results

Wightman Fields for Two-Dimensional Conformal Field Theories with Pointed Representation Category

Two-dimensional full conformal field theories have been studied in various mathematical frameworks, from algebraic, operator-algebraic to categorical. In this work, we focus our attention on theories with chiral components having pointed braided tensor representation subcategories, namely having automorphisms whose equivalence classes necessarily form an abelian group. For such theories, we exhibit the explicit Hilbert space structure and construct primary fields as Wightman fields for the two-dimensional full theory. Given a finite collection of chiral components with automorphism categories with trivial total braiding, we also construct a local extension of their tensor product as a chiral component. We clarify the relations with the Longo-Rehren construction, and illustrate these results with concrete examples including the U(1)current