Empowering Telco operator convergence through a common marketplace

2010 ◽  
Author(s):  
Simon Becot ◽  
Ivan Bedini ◽  
Mariano Belaunde ◽  
Santiago Perez Marin ◽  
Oscar Lorenzo Duenas Rugnon ◽  
...  
Keyword(s):  
Operator Convergence

scholarly journals Fuzzy Counterparts of Fischer Diagonal Condition in ⊤-Convergence Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 685
Author(s):  
Qiu Jin ◽  
Lingqiang Li ◽  
Jing Jiang
Keyword(s):  
Topological Space ◽  
Fuzzy Topology ◽  
Convergence Space ◽  
Convergence Spaces ◽  
Different Types ◽  
Diagonal Condition ◽  
Operator Convergence

Fischer diagonal condition plays an important role in convergence space since it precisely ensures a convergence space to be a topological space. Generally, Fischer diagonal condition can be represented equivalently both by Kowalsky compression operator and Gähler compression operator. ⊤-convergence spaces are fundamental fuzzy extensions of convergence spaces. Quite recently, by extending Gähler compression operator to fuzzy case, Fang and Yue proposed a fuzzy counterpart of Fischer diagonal condition, and proved that ⊤-convergence space with their Fischer diagonal condition just characterizes strong L-topology—a type of fuzzy topology. In this paper, by extending the Kowalsky compression operator, we present a fuzzy counterpart of Fischer diagonal condition, and verify that a ⊤-convergence space with our Fischer diagonal condition precisely characterizes topological generated L-topology—a type of fuzzy topology. Hence, although the crisp Fischer diagonal conditions based on the Kowalsky compression operator and the on Gähler compression operator are equivalent, their fuzzy counterparts are not equivalent since they describe different types of fuzzy topologies. This indicates that the fuzzy topology (convergence) is more complex and varied than the crisp topology (convergence).

ENTROPY DENSITIES FOR GIBBS STATES OF QUANTUM SPIN SYSTEMS

1993 ◽  
Vol 05 (04) ◽  
pp. 693-712 ◽  
Author(s):  
FUMIO HIAI ◽  
DÉNES PETZ
Keyword(s):  
General Theory ◽  
Quantum Spin ◽  
Spin Systems ◽  
Gibbs States ◽  
Quantum Spin Systems ◽  
Short Discussion ◽  
Range Interaction ◽  
Asymptotic Equipartition Property ◽  
The Mean ◽  
Operator Convergence

This paper is a contribution to the general theory of quantum spin systems. We deal with a general theory in the sense that no concrete interaction shows up but an arbitrary relatively short-range interaction is chosen. It is well known that the mean entropy plays an important role in the thermodynamics of quantum spin systems: it is one of the ingredients of the Lanford–Ruelle–Robinson variational principle. We show that in the background of the existence of the mean entropy, there is an operator convergence which resembles the McMillan theorem from information theory. Asymptotic equipartition property and several entropy densities are investigated, in particular, the relation of the Gibbs condition to relative entropies. Although this paper is not intended to be a review, we try to give an overview of the theory of quantum Gibbs states in the mathematical sense. The paper is organized as follows. Section 1 provides an introduction and further sections contain our new results. Each section is closed with a short discussion on sources and references.

scholarly journals A Two Dimensional Discrete Mollification Operator and the Numerical Solution of an Inverse Source Problem

Axioms ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 89 ◽  
Author(s):  
Manuel Echeverry ◽  
Carlos Mejía
Keyword(s):  
Inverse Problem ◽  
Source Term ◽  
Fractional Diffusion ◽  
Inverse Source Problem ◽  
Two Dimensional ◽  
Regularization Procedure ◽  
Numerical Examples ◽  
Convergence Results ◽  
Time Fractional Diffusion Equation ◽  
Operator Convergence

We consider a two-dimensional time fractional diffusion equation and address the important inverse problem consisting of the identification of an ingredient in the source term. The fractional derivative is in the sense of Caputo. The necessary regularization procedure is provided by a two-dimensional discrete mollification operator. Convergence results and illustrative numerical examples are included.

On operator convergence in Hilbert space and in Lebesgue space

1972 ◽  
Vol 2 (1-4) ◽  
pp. 235-244 ◽  
Author(s):  
M. Akcoglu ◽  
L. Sucheston
Keyword(s):  
Hilbert Space ◽  
Lebesgue Space ◽  
Operator Convergence

scholarly journals Generalized Multipliers for Left-Invertible Operators and Applications

2020 ◽  
Vol 92 (5) ◽  
Author(s):  
Paweł Pietrzycki
Keyword(s):  
Analytic Functions ◽  
Laurent Series ◽  
Invertible Operator ◽  
Weighted Shift ◽  
Multiplication Operators ◽  
Formal Laurent Series ◽  
Directed Tree ◽  
Generalized Multipliers ◽  
Weak Operator ◽  
Operator Convergence

Abstract Generalized multipliers for a left-invertible operator T, whose formal Laurent series $$U_x(z)=\sum _{n=1}^\infty (P_ET^{n}x)\frac{1}{z^n}+\sum _{n=0}^\infty (P_E{T^{\prime *n}}x)z^n$$ U x ( z ) = ∑ n = 1 ∞ ( P E T n x ) 1 z n + ∑ n = 0 ∞ ( P E T ′ ∗ n x ) z n , $$x\in \mathcal {H}$$ x ∈ H actually represent analytic functions on an annulus or a disc are investigated. We show that they are coefficients of analytic functions and characterize the commutant of some left-invertible operators, which satisfies certain conditions in its terms. In addition, we prove that the set of multiplication operators associated with a weighted shift on a rootless directed tree lies in the closure of polynomials in z and $$\frac{1}{z}$$ 1 z of the weighted shift in the topologies of strong and weak operator convergence.

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