Search results for "C*-algebra"
showing 10 items of 67 documents
The spectra of some algebras of analytic mappings
1999
Abstract Let E be a Banach space with the approximation property and let F be a Banach algebra with identity. We study the spectrum of the algebra H b(E, F) of all holomorphic mappings f : E → F that are bounded on the bounded subsets of E.
Representable linear functionals on partial *-algebras
2012
A GNS-like *-representation of a partial *-algebra \({{\mathfrak A}}\) defined by certain representable linear functionals on \({{\mathfrak A}}\) is constructed. The study of the interplay with the GNS construction associated with invariant positive sesquilinear forms (ips) leads to the notions of pre-core and of singular form. It is shown that a positive sesquilinear form with pre-core always decomposes into the sum of an ips form and a singular one.
WQ*-algebras of measurable operators
2012
Every C*-algebra \(\mathfrak{A}\) has a faithful *-representation π in a Hilbert space \(\mathcal{H}\). Consequently it is natural to pose the following question: under which conditions, the completion of a C*-algebra in a weaker than the given one topology, can be realized as a quasi *-algebra of operators? The present paper presents the possibility of extending the well known Gelfand — Naimark representation of C*-algebras to certain Banach C*-modules.
Locally convex quasi *-algebras with sufficiently many *-representations
2012
AbstractThe main aim of this paper is the investigation of conditions under which a locally convex quasi ⁎-algebra (A[τ],A0) attains sufficiently many (τ,tw)-continuous ⁎-representations in L†(D,H), to separate its points. Having achieved this, a usual notion of bounded elements on A[τ] rises. On the other hand, a natural order exists on (A[τ],A0) related to the topology τ, that also leads to a kind of bounded elements, which we call “order bounded”. What is important is that under certain conditions the latter notion of boundedness coincides with the usual one. Several nice properties of order bounded elements are extracted that enrich the structure of locally convex quasi ⁎-algebras.
Duality, projectivity, and unification in Łukasiewicz logic and MV-algebras
2013
AbstractWe prove that the unification type of Łukasiewicz (infinite-valued propositional) logic and of its equivalent algebraic semantics, the variety of MV-algebras, is nullary. The proof rests upon Ghilardiʼs algebraic characterisation of unification types in terms of projective objects, recent progress by Cabrer and Mundici in the investigation of projective MV-algebras, the categorical duality between finitely presented MV-algebras and rational polyhedra, and, finally, a homotopy-theoretic argument that exploits lifts of continuous maps to the universal covering space of the circle. We discuss the background to such diverse tools. In particular, we offer a detailed proof of the duality …
The Cognitive Demand of a Gifted Student’s Answers to Geometric Pattern Problems
2018
Mathematically gifted students require specific teaching methodologies to foster their interest in mathematics and their engagement in solving problems. Geometric pattern problems are an interesting context in which to introduce algebra to those students. We present the case of a nine-year-old student engaged in a teaching unit based on geometric pattern problems that was aimed at helping him start learning algebra, equations, and algebra word problems. To analyze and assess the cognitive effort the student made to solve the problems, we used a particularization to this context of the cognitive demand model. We analyzed answers typical of the different kinds of problems posed throughout the…
Instanton Counting, Quantum Geometry and Algebra
2020
The aim of this memoir for "Habilitation \`a Diriger des Recherches" is to present quantum geometric and algebraic aspects of supersymmetric gauge theory, which emerge from non-perturbative nature of the vacuum structure induced by instantons. We start with a brief summary of the equivariant localization of the instanton moduli space, and show how to obtain the instanton partition function and its generalization to quiver gauge theory and supergroup gauge theory in three ways: the equivariant index formula, the contour integral formula, and the combinatorial formula. We then explore the geometric description of $\mathcal{N} = 2$ gauge theory based on Seiberg-Witten geometry together with it…
Integrating over quiver variety and BPS/CFT correspondence
2019
We show the vertex operator formalism for the quiver gauge theory partition function and the $qq$-character of highest-weight module on quiver, both associated with the integral over the quiver variety.
Automated vehicles' work planning in flexible manufacturing systems
2006
The problem of rules setting in coordination of automated vehicles access to shared system resources (sections of their transportation paths) which assure a deadlock free and starvation free flow of the executed processes belongs to NP-hard problems. Assuming that there are local (controlling access to shared resources) rules of priority dispatching, the problem deals with setting conditions sufficient for a pair (initial state, set of priority dispatching rules). The assumed knowledge base way of specifying a transportation subsystem leads to solving a logic-algebraic method decision problem. In this regard, the working knowledge representation synthesis method constitutes a significant co…
Representable states on quasilocal quasi *-algebras
2011
Continuing a previous analysis originally motivated by physics, we consider representable states on quasi-local quasi *-algebras, starting with examining the possibility for a {\em compatible} family of {\em local} states to give rise to a {\em global} state. Some properties of {\em local modifications} of representable states and some aspects of their asymptotic behavior are also considered.