Search results for "Operator theory"
showing 10 items of 95 documents
Deformations of Differential Calculi
1996
It has been suggested that quantum fluctuations of the gravitational field could give rise in the lowest approximation to an effective noncommutative version of Kaluza-Klein theory which has as extra hidden structure a noncommutative geometry. It would seem however from the Standard Model, at least as far as the weak interactions are concerned, that a double-sheeted structure is the phenomenologically appropriate one at present accelerator energies. We examine here to what extent this latter structure can be considered as a singular limit of the former.
Symmetric-group approach to the study of the traces ofp-order reduced-density operators and of products of these operators
1990
In this work we give the values of traces of p-order reduced-density operators. These traces are obtained by application of the spin functions and of the symmetric-group properties. The relations obtained here will allow an easy and fast evaluation of the high-order spin-adapted reduced Hamiltonian matrix elements and high-order Hamiltonian moments.
Some spectral properties for operators acting on Rigged Hilbert spaces
2015
Operators on Rigged Hilbert spaces have been considered from the 80s of the 20th century on as good ones for describing several physical models whose observable set didn’t turn out to be a C∗-algebra.A notion of resolvent set for an operator acting in a rigged Hilbert space \(\mathcal{D}\subset \mathcal{H}\subset \mathcal{D}^{\times }\) is proposed. This set depends on a family of intermediate locally convex spaces living between \(\mathcal{D}\) and \(\mathcal{D}^{\times }\), called interspaces. Some properties of the resolvent set and of the corresponding multivalued resolvent function are derived and some examples are discussed.
Model pseudofermionic systems: Connections with exceptional points
2014
We discuss the role of pseudo-fermions in the analysis of some two-dimensional models, recently introduced in connection with non self-adjoint hamiltonians. Among other aspects, we discuss the appearance of exceptional points in connection with the validity of the extended anti-commutation rules which define the pseudo-fermionic structure.
γ‐Agregation operators and some aspects of generalized aggregation problem
2010
We explore questions related to the aggregation operators and aggregation of fuzzy sets. No preliminary knowledge of the aggregation operators theory and of the fuzzy sets theory are required, because all necessary information is given in Section 2. Later we introduce a new class of γ‐aggregation operators, which “ignore” arguments less than γ. Due to this property γ‐aggregation operators simplify the aggregation process and extend the area of possible applications. The second part of the paper is devoted to the generalized aggregation problem. We use the definition of generalized aggregation operator, introduced by A. Takaci in [7], and study the pointwise extension of a γ‐agop. First publ…
The class of F-contraction mappings with a measure of noncompactness
2017
In this chapter we review a class of contraction conditions, which are largely used to obtain interesting generalizations of the Banach fixed-point theorem in various abstract settings. We also present a new fixed-point existence result obtained by considering such a kind of contraction condition and a measure of noncompactness. Moreover, we show the applicability of these results in the theory of functional equations.
On symplectically rigid local systems of rank four and Calabi–Yau operators
2013
AbstractWe classify all Sp4(C)-rigid, quasi-unipotent local systems and show that all of them have geometric origin. Furthermore, we investigate which of those having a maximal unipotent element are induced by fourth order Calabi–Yau operators. Via this approach, we reconstruct all known Calabi–Yau operators inducing an Sp4(C)-rigid monodromy tuple and obtain closed formulae for special solutions of them.
Partial Multiplication of Operators in Rigged Hilbert Spaces
2005
The problem of the multiplication of operators acting in rigged Hilbert spaces is considered. This is done, as usual, by constructing certain intermediate spaces through which the product can be factorized. In the special case where the starting space is the set of C∞-vectors of a self-adjoint operator A, a general procedure for constructing a special family of interspaces is given. Their definition closely reminds that of the Bessel potential spaces, to which they reduce when the starting space is the Schwartz space \(\mathcal{S}(\mathbb{R}^n ).\) Some applications are considered.
A fixed point theorem for a Meir-Keeler type contraction through rational expression
2013
In this paper, we establish a new fixed point theorem for a Meir-Keeler type contraction through rational expression. The presented theorem is an extension of the result of Dass and Gupta (1975). Some applications to contractions of integral type are given.
Extensions of the Noncommutative Integration
2016
In this paper we will continue the analysis undertaken in Bagarello et al. (Rend Circ Mat Palermo (2) 55:21–28, 2006), Bongiorno et al. (Rocky Mt J Math 40(6):1745–1777, 2010), Triolo (Rend Circ Mat Palermo (2) 60(3):409–416, 2011) on the general problem of extending the noncommutative integration in a *-algebra of measurable operators. As in Aiena et al. (Filomat 28(2):263–273, 2014), Bagarello (Stud Math 172(3):289–305, 2006) and Bagarello et al. (Rend Circ Mat Palermo (2) 55:21–28, 2006), the main problem is to represent different types of partial *-algebras into a *-algebra of measurable operators in Segal’s sense, provided that these partial *-algebras posses a sufficient family of pos…