Search results for "operator algebras"
showing 10 items of 71 documents
Current Algebras as Hilbert Space Operator Cocycles
1994
Aspects of a generalized representation theory of current algebras in 3 + 1 dimensions axe discussed. Rules for a systematic computation of vacuum expectation values of products of currents are described. Their relation to gauge group actions in bundles of fermionic Fock spaces and to the sesquilinear form approach of Langmann and Ruijsenaars is explained. The regularization for a construction of an operator cocycle representation of the current algebra is explained. An alternative formula for the Schwinger terms defining gauge group extensions is written in terms of Wodzicki residue and Dixmier trace.
Representable and Continuous Functionals on Banach Quasi *-Algebras
2017
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.
THE CAUCHY DUAL AND 2-ISOMETRIC LIFTINGS OF CONCAVE OPERATORS
2018
We present some 2-isometric lifting and extension results for Hilbert space concave operators. For a special class of concave operators we study their Cauchy dual operators and discuss conditions under which these operators are subnormal. In particular, the quasinormality of compressions of such operators is studied.
Complex powers and non-compact manifolds
2002
We study the complex powers $A^{z}$ of an elliptic, strictly positive pseudodifferential operator $A$ using an axiomatic method that combines the approaches of Guillemin and Seeley. In particular, we introduce a class of algebras, ``extended Weyl algebras,'' whose definition was inspired by Guillemin's paper on the subject. An extended Weyl algebra can be thought of as an algebra of ``abstract pseudodifferential operators.'' Many algebras of pseudodifferential operators are extended Weyl algebras. Several results typical for algebras of pseudodifferential operators (asymptotic completeness, construction of Sobolev spaces, boundedness between apropriate Sobolev spaces, >...) generalize to…
Weak commutation relations of unbounded operators and applications
2011
Four possible definitions of the commutation relation $[S,T]=\Id$ of two closable unbounded operators $S,T$ are compared. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the operators act. Some consequences on the existence of eigenvectors of two number-like operators are derived and the partial O*-algebra generated by $S,T$ is studied. Some applications are also considered.
Symmetrization for singular semilinear elliptic equations
2012
In this paper, we prove some comparison results for the solution to a Dirichlet problem associated with a singular elliptic equation and we study how the summability of such a solution varies depending on the summability of the datum f. © 2012 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.
Fixed Points in Topological *-Algebras of Unbounded Operators
2001
We discuss some results concerning fixed point equations in the setting of topological *-algebras of unbounded operators. In particular, an existence result is obtained for what we have called {\em weak $\tau$ strict contractions}, and some continuity properties of these maps are discussed. We also discuss possible applications of our procedure to quantum mechanical systems.
Periodic Groups Covered by Transitive Subgroups of Finitary Permutations or by Irreducible Subgroups of Finitary Transformations
1999
Let X be either the class of all transitive groups of finitary permutations, or the class of all periodic irreducible finitary linear groups. We show that almost primitive X-groups are countably recognizable, while totally imprimitive X-groups are in general not countably recognizable. In addition we derive a structure theorem for groups all of whose countable subsets are contained in totally imprimitive X-subgroups. It turns out that totally imprimitive p-groups in the class X are countably recognizable.
L 2-topological invariants of 3-manifolds
1995
We give results on theL2-Betti numbers and Novikov-Shubin invariants of compact manifolds, especially 3-manifolds. We first study the Betti numbers and Novikov-Shubin invariants of a chain complex of Hilbert modules over a finite von Neumann algebra. We establish inequalities among the Novikov-Shubin invariants of the terms in a short exact sequence of chain complexes. Our algebraic results, along with some analytic results on geometric 3-manifolds, are used to compute theL2-Betti numbers of compact 3-manifolds which satisfy a weak form of the geometrization conjecture, and to compute or estimate their Novikov-Shubin invariants.
On generalized a-Browder's theorem
2007
We characterize the bounded linear operators T satisfying generalized a-Browder's theorem, or generalized a-Weyl's theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H0(�I T) asbelongs to certain sets of C. In the last part we give a general framework in which generalized a-Weyl's theorem follows for several classes of operators. 1. Preliminaries. Let L(X) denote the space of bounded linear oper- ators on an infinite-dimensional complex Banach space X. For T ∈ L(X), denote by α(T) the dimension of the kernel ker T, and by β(T) the codi- mension of the range T(X). The operator T ∈ L(X) is called upper semi- Fredholm if α(T) < ∞ and T(X) is closed, and lower …