Self-adjoint Research Articles

The Minimum Numbers for Certain Positive Operators

In this paper we give upper and lower bounds of the infimum of k  such that kI+2ReT⊗Sm  is positive, where Sm  is the m×m  matrix whose entries are all 0’s except on the superdiagonal where they are all 1’s and T∈BH  for some Hilbert space H. 
 
 When T  is self-adjoint, we have the minimum of k. 
 
 When m=3  and T∈B(H)  , we obtain the minimum of k  and an inequality
 
 Involving the numerical radius w(T) .

Explicit group AOR method for solving elliptic partial differential equations

The explicit group overrelaxation methods for the numerical solution of the sparse linear systems derived from the discretisation of self-adjoint elliptic partial differential equations have been presented (Yousif & Evans, 1986) and has been shown to be computationally superior in comparison with the implicit 1-line and 2-line block succsessive overrelaxation (SOR) iterative methods. In this work a new explicit 4-point group accelerated overrelaxation (Group AOR) iterative method is presented. A comparison with the point AOR method for the model problem shows the computational advantages of the new technique.

Non-linear $\lambda $-Jordan triple $\ast $-derivation on prime $\ast $-algebras

Let $\mathcal {A}$ be a prime $\ast $-algebra and $\Phi $ a $\lambda $-Jordan triple derivation on $A$, that is, for every $A,B,C \in \mathcal {A}$, $$\Phi (A\diamond _{\lambda } B \diamond _{\lambda }C)=\Phi (A)\diamond _{\lambda }B\diamond _{\lambda } C+A\diamond _{\lambda }\Phi (B)\diamond _{\lambda }C+A\diamond _{\lambda } B\diamond _{\lambda }\Phi (C),$$ where $A\diamond _{\lambda } B = AB + \lambda BA^{\ast }$ such that a complex scalar $|\lambda |\neq 0,1$, and $\Phi $ is additive. Moreover, if $\Phi (I)$ is self-adjoint, then $\Phi $ is a $\ast $-derivation.

MERCER–TRAPEZOID RULE FOR THE RIEMANN–STIELTJES INTEGRAL WITH APPLICATIONS

In this paper several new error bounds for the Mercer–Trapezoid quadrature rule for the Riemann-Stieltjesintegral under various assumptions are proved. Applications for functions of selfadjoint operators on complexHilbert spaces are provided as well.

Schur–Horn theorems in II∞-factors

Fil: Massey, Pedro Gustavo. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina

The Lagrange Mechanization and Application of Multi-Machine Power System

The fast development of Hamilton system theory provides a powerful tool for the nonlinear control and stability analysis of power system. The construction of Hamilton function plays an important role in Hamilton realization. Based on Hamilton canonical equations, the energy integration of system is given. This paper expands the odd-order power system to even-order system and gives the responding conditions of Hamilton realization by using the self-adjoint methods of analytical mechanics. Besides, the standard Hamilton form of power system is derived by the combinations of Lagrange mechanization and Hamilton theory, and the form of Hamilton function is also given. Based on non-conservative analytical mechanical principles, the controllers are designed in allusion to the characteristics of power system and Matlab program is realized in IEEE3-9 standard system. The simulation effects are discussed in the transient conditions of three-phase fault by comparison of different approaches, which proves the effectiveness of the control strategy. This approach to construct Hamilton function and design the controllers has an extensive prospect of application

User-Friendly Tail Bounds for Sums of Random Matrices

This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they delive...

Metrics in the sphere of a C*-module

Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Oficina de Coordinacion Administrativa Saavedra 15. Instituto Argentino de Matematica Alberto Calderon; Argentina

Von Neumann J-algebras in a space with two symmetries

We show that a von Neumann J-algebra A of type (B) does not contain J-positive (J-negative) operators. J-projections in A are characterized. The class of plus-operators that are simultaneously self-adjoint and J-self-adjoint is described.

ADDITIVITY OF JORDAN MULTIPLICATIVE MAPS ON JORDAN OPERATOR ALGEBRAS

Let H be a Hilbert space and N a nest in H. Denote by Sa(H) the Jordan ring of all self-adjoint operators on H and AlgN the nest algebra associated to N. We show that a bijective map Φ : Sa(H) → Sa(H) satisfying (1) Φ(ABA) = Φ(A)Φ(B)Φ(A) for every pair of A,B, or (2) Φ(AB + BA) = Φ(A)Φ(B) + Φ(B)Φ(A) for every pair of A,B, or (3) Φ(1 2 (AB +BA)) = 1 2 (Φ(A)Φ(B)+Φ(B)Φ(A)) for every pair of A,B must be additive, that is, a Jordan ring isomorphism. We also show that if a bijective map Φ : AlgN → AlgN satisfies the Jordan multiplicativity of the form (2) or (3), then Φ must be a Jordan isomorphism. Moreover, such Jordan multiplicative maps are characterized completely.

On the nonnegativity of operator products

A bounded, not necessarily everywhere defined, nonnegative operator A in a Hilbert space \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\mathfrak{H}$ \end{document} is assumed to intertwine in a certain sense two bounded everywhere defined operators B and C. If the range of A is provided with a natural inner product then the operators B and C induce two new operators on the completion space. This construction is used to show the existence of selfadjoint and nonnegative extensions of B*A and C*A.

Strongly Supercommuting Self-Adjoint Operators

We introduce the notion of strong supercommutativity of self-adjoint operators on a % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf % gDOjdaryqr1ngBPrginfgDObcv39gaiuaacqWFKeIwdaWgaaWcbaGa % aGOmaaqabaaaaa!419D! $$\mathbb{Z}_2 $$ -graded Hilbert space and give some basic properties. We clarify that strong supercommutativity is a unification of strong commutativity and strong anticommutativity. We also establish the theory of super quantization. Applications to supersymmetric quantum field theory and a fermion-boson interaction system are discussed.

On the Positivity of the Jansen-Heß Operator for Arbitrary Mass

Iantchenko, A.; Jakubasa-Amundsen, D.H., (2003) 'On the positivity of the Jansen-Hes operator for arbitrary mass', Annales of the Institute Henri Poincare 4 pp.1083-1099 RAE2008

Linear resolvent growth of rank one perturbation of a unitary operator does not imply its similarity to a normal operator

The main result of this paper is that for any unitary (selfadjoint) operatorU with non-trivial absolutely continuous part of the spectrum, there exists a rank-one perturbationK = ba* = (a)b such that the operatorT = U + K satisfies the Linear Resolvent Growth condition (LRG), % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfKttLearuqr1ngBPrgarmqr1ngBPrgitL% xBI9gBamXvP5wqSXMqHnxAJn0BKvguHDwzZbqegm0B1jxALjhiov2D% aeHbuLwBLnhiov2DGi1BTfMBaebbfv3ySLgzGueE0jxyaibaiiYdf9% irVeeu0dXdh9vqqj-hEeeu0xXdbba9frFj0-OqFfea0dXdd9vqaq-J% frVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabi% GaciaacaqabeaadaabauaaaOqaaiabcYha8jabcYha8jabcIcaOiab% eU7aSjabdMeajjabgkHiTiabdsfaujabcMcaPmaaCaaaleqabaGaey% OeI0IaeGymaedaaOGaeiiFaWNaeiiFaWNaeyizImQaem4qamKaei4l% a8ccbaGae8hzaqMae8xAaKMae83CamNae8hDaqNae8hkaGIaeq4UdW% Mae8hlaWIaeq4WdmNae8hkaGccbiGae4hvaqLae8xkaKIae8xkaKIa% e8hlaWsegeKCPfgBaGGbciaa9bcacaqFGaGaa0hiaiaa9bcacaqFGa% Gaa0hiaiaa9bcacqaH7oaBcqGHiiIZiuaacqaFceYOcqWFCbaxcqaH% dpWCcqWFOaakcqGFubavcqWFPaqkcqWFSaalaaa!7224! $$||(\lambda I - T)^{ - 1} || \leqslant C/dist(\lambda ,\sigma (T)), \lambda \in \mathbb{C}\backslash \sigma (T),$$ its spectrum lies on the unit circle T (on the real line ℝ), butT is not similar to a normal operator. This contrasts sharply with the result of M. Benamara and the first author [1] that if a finite rank perturbationT = U + K of a unitary operator is acontraction (¦T¦< 1), then it is similar to a normal operator if and only if it satisfies (LRG) and its spectrum does not cover the unit disc D.

Polar decomposition under perturbations of the scalar product

Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Oficina de Coordinacion Administrativa Saavedra 15. Instituto Argentino de Matematica Alberto Calderon; Argentina

Self-adjoint ideals in baer *-rings

(2000). Self-adjoint ideals in baer *-rings. Communications in Algebra: Vol. 28, No. 9, pp. 4259-4268.

An application of the exponential cubic splines to numerical solution of a self-adjoint perturbation problem

We present a class of the second order optimal splines difference schemes derived from expomential cubic splines for self-adjoint singularly perturbed 2-point boundary value problem. We prove an optimal error estimate and give illustrative numerical example.

Spectral study of a self-adjoint operator on $L^2 (\Omega)$ related with a Poincaré type constant

Soit un ouvert borne et connexe de R N , N > 2, de frontiere lipschitzienne. L'espace H 0 1 (Ω) est muni de la norme du gradient. L'inegalite suivante a lieu pour les elements de L 2 (Ω). ...Formula math... ou C(Ω) > 0 ne depend que de Ω. A l'aide d'un operateur autoadjoint sur L 2 (Ω), on caracterise la meilleure constante dans l'inegalite precedente. Lorsque Ω est une boule de R N , N ≥ 2, on fait l'analyse spectrale de cet operateur et on montre que la meilleure valeur de la constante est N.

Kneser-type oscillation criteria for self-adjoint two-term differential equations

It is proved that the even-order equationy (2n) +p(t)y=0 is (n,n) oscillatory at ∞ if $$\mathop {\lim }\limits_{t \to \infty } ( - 1)^n \log t\int_t^\infty {s^{2n - 1} } \left( {p(s) + \frac{{\mu _{2n} }}{{s^{2n} }}} \right) ds< - K_n $$ , where $$K_n = ( - 1)^{n - 1} \tfrac{1}{2}\tfrac{{d^2 }}{{d\lambda ^2 }}P_{2n} (\lambda )|_{\lambda = \tfrac{{2n - 1}}{2}} , P(\lambda ) = (\lambda - 1) \ldots (\lambda - 2n + 1), \mu _{2n} = P\left( {\tfrac{{2n - 1}}{2}} \right)$$

Necessary conditions for similarity of an operator to a self-adjoint one

Necessary conditions for similarity of an operator to a self-adjoint one