scholarly journals Primal-dual algorithms and infinite-dimensional Jordan algebras of finite rank

2003 ◽  
Vol 97 (3) ◽  
pp. 471-493 ◽  
Author(s):  
Leonid Faybusovich ◽  
Takashi Tsuchiya
Keyword(s):  
Finite Rank ◽  
Jordan Algebras ◽  
Infinite Dimensional ◽  
Primal Dual

Primal-Dual Methods for Solving Infinite-Dimensional Games

2015 ◽  
Vol 166 (1) ◽  
pp. 23-51 ◽  
Author(s):  
Pavel Dvurechensky ◽  
Yurii Nesterov ◽  
Vladimir Spokoiny
Keyword(s):  
Infinite Dimensional ◽  
Dual Methods ◽  
Primal Dual

scholarly journals VARIATIONS OF BPS STRUCTURE AND A LARGE RANK LIMIT

2019 ◽  
pp. 1-33 ◽  
Author(s):  
Jacopo Scalise ◽  
Jacopo Stoppa
Keyword(s):  
Partition Function ◽  
Differential Equations ◽  
Finite Rank ◽  
Large Rank ◽  
Infinite Dimensional ◽  
Positive Degree

We study a class of flat bundles, of finite rank$N$, which arise naturally from the Donaldson–Thomas theory of a Calabi–Yau threefold$X$via the notion of a variation of BPS structure. We prove that in a large$N$limit their flat sections converge to the solutions to certain infinite-dimensional Riemann–Hilbert problems recently found by Bridgeland. In particular this implies an expression for the positive degree, genus 0 Gopakumar–Vafa contribution to the Gromov–Witten partition function of$X$in terms of solutions to confluent hypergeometric differential equations.

scholarly journals Localization and computation in an approximation of eigenvalues

Filomat ◽  
2015 ◽  
Vol 29 (1) ◽  
pp. 75-81
Author(s):  
S.V. Djordjevic ◽  
G. Kantún-Montiel
Keyword(s):  
Hilbert Spaces ◽  
Finite Rank ◽  
Vector Spaces ◽  
Dimensional Case ◽  
Dimensional Vector ◽  
Infinite Dimensional ◽  
Weyl Spectrum ◽  
Isolated Points ◽  
Isolated Point ◽  
Different Parts

In this note we consider the problem of localization and approximation of eigenvalues of operators on infinite dimensional Banach and Hilbert spaces. This problem has been studied for operators of finite rank but it is seldom investigated in the infinite dimensional case. The eigenvalues of an operator (between infinite dimensional vector spaces) can be positioned in different parts of the spectrum of the operator, even it is not necessary to be isolated points in the spectrum. Also, an isolated point in the spectrum is not necessary an eigenvalue. One method that we can apply is using Weyl?s theorem for an operator, which asserts that every point outside the Weyl spectrum is an isolated eigenvalue.

Hilbert space methods in the theory of Jordan algebras. I

1975 ◽  
Vol 78 (2) ◽  
pp. 293-300 ◽  
Author(s):  
C. Viola Devapakkiam
Keyword(s):  
Hilbert Space ◽  
Classification Problem ◽  
Jordan Algebras ◽  
Inner Product ◽  
Uniqueness Problem ◽  
Associative Algebras ◽  
Infinite Dimensional

In this paper, we study the structure of certain infinite-dimensional Jordan algebras admitting an inner product. These algebras, called J*-algebras in the sequel, have already been considered in (4) in connexion with the norm uniqueness problem for non-associative algebras. We deal here with the structure and classification of these algebras. Existence of self-adjoint idempotents plays a central role in the classification problem.

scholarly journals On Pre-Hilbert Noncommutative Jordan Algebras Satisfying

ISRN Algebra ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Mohamed Benslimane ◽  
Abdelhadi Moutassim
Keyword(s):  
Vector Space ◽  
Associative Algebra ◽  
Jordan Algebra ◽  
Alternative Algebra ◽  
Jordan Algebras ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
First Case ◽  
Hilbert Norm ◽  
Complex Powers

Let be a real or complex algebra. Assuming that a vector space is endowed with a pre-Hilbert norm satisfying for all . We prove that is finite dimensional in the following cases. (1) is a real weakly alternative algebra without divisors of zero. (2) is a complex powers associative algebra. (3) is a complex flexible algebraic algebra. (4) is a complex Jordan algebra. In the first case is isomorphic to or and is isomorphic to in the last three cases. These last cases permit us to show that if is a complex pre-Hilbert noncommutative Jordan algebra satisfying for all , then is finite dimensional and is isomorphic to . Moreover, we give an example of an infinite-dimensional real pre-Hilbert Jordan algebra with divisors of zero and satisfying for all .

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