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Adjoint Operator
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Matthias Langer – One of the best experts on this subject based on the ideXlab platform.

Triple variational principles for selfAdjoint Operator functions
Journal of Functional Analysis, 2016CoAuthors: Matthias Langer, Michael StraussAbstract:For a very general class of unbounded selfAdjoint Operator function we prove upper bounds for eigenvalues which lie within arbitrary gaps of the essential spectrum. These upper bounds are given by triple variations. Furthermore, we find conditions which imply that a point is in the resolvent set. For norm resolvent continuous Operator functions we show that the variational inequality becomes an equality.

the virozub matsaev condition and spectrum of definite type for self Adjoint Operator functions
Complex Analysis and Operator Theory, 2008CoAuthors: Matthias Langer, Heinz Langer, Alexander Markus, Christiane TretterAbstract:We establish sufficient conditions for the socalled Virozub–Matsaev condition for twice continuously differentiable selfAdjoint Operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to selfAdjoint Operators in Krein spaces and to quadratic Operator polynomials are given.

The Virozub–Matsaev Condition and Spectrum of Definite Type for SelfAdjoint Operator Functions
Complex Analysis and Operator Theory, 2007CoAuthors: Matthias Langer, Heinz Langer, Alexander Markus, Christiane TretterAbstract:We establish sufficient conditions for the socalled Virozub–Matsaev condition for twice continuously differentiable selfAdjoint Operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to selfAdjoint Operators in Krein spaces and to quadratic Operator polynomials are given.
Heinz Langer – One of the best experts on this subject based on the ideXlab platform.

the virozub matsaev condition and spectrum of definite type for self Adjoint Operator functions
Complex Analysis and Operator Theory, 2008CoAuthors: Matthias Langer, Heinz Langer, Alexander Markus, Christiane TretterAbstract:We establish sufficient conditions for the socalled Virozub–Matsaev condition for twice continuously differentiable selfAdjoint Operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to selfAdjoint Operators in Krein spaces and to quadratic Operator polynomials are given.

The Virozub–Matsaev Condition and Spectrum of Definite Type for SelfAdjoint Operator Functions
Complex Analysis and Operator Theory, 2007CoAuthors: Matthias Langer, Heinz Langer, Alexander Markus, Christiane TretterAbstract:We establish sufficient conditions for the socalled Virozub–Matsaev condition for twice continuously differentiable selfAdjoint Operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to selfAdjoint Operators in Krein spaces and to quadratic Operator polynomials are given.

the schur transformation for generalized nevanlinna functions interpolation and self Adjoint Operator realizations
Complex Analysis and Operator Theory, 2007CoAuthors: Daniel Alpay, Heinz Langer, Aad Dijksma, Yuri ShondinAbstract:The Schur transformation for generalized Nevanlinna functions has been defined and applied in [2]. In this paper we discuss its relation to a basic interpolation problem and study its effect on the minimal selfAdjoint Operator (or relation) realization of a generalized Nevanlinna function.
George A. Anastassiou – One of the best experts on this subject based on the ideXlab platform.

Fractional Conformable Self Adjoint Operator Analytic Inequalities
Intelligent Analysis: Fractional Inequalities and Approximations Expanded, 2020CoAuthors: George A. AnastassiouAbstract:We present here conformable fractional self Adjoint Operator comparison, Poincare, Sobolev, Ostrowski and Opial type inequalities. At first we give right and left conformable fractional representation formulae in the self Adjoint Operator sense. Operator inequalities are based in the self Adjoint Operator order over a Hilbert space. See also [3].

Self Adjoint Operator Korovkin Type Quantitative Approximation Theory
Intelligent Comparisons II: Operator Inequalities and Approximations, 2017CoAuthors: George A. AnastassiouAbstract:Here we present self Adjoint Operator Korovkin type theorems, via self Adjoint Operator ShishaMond type inequalities. This is a quantitative treatment to determine the degree of self Adjoint Operator uniform approximation with rates, of sequences of self Adjoint Operator positive linear Operators. We give several applications involving the self Adjoint Operator Bernstein polynomials. It follows [2].

Self Adjoint Operator Korovkin and Polynomial Direct Approximations with Rates
Intelligent Comparisons II: Operator Inequalities and Approximations, 2017CoAuthors: George A. AnastassiouAbstract:Here we present self Adjoint Operator Korovkin type theorems, via self Adjoint Operator ShishaMond type inequalities, also we give self Adjoint Operator polynomial approximations. This is a quantitative treatment to determine the degree of self Adjoint Operator uniform approximation with rates, of sequences of self Adjoint Operator positive linear Operators. The same kind of work is performed over important Operator polynomial sequences. Our approach is direct based on Gelfand isometry. It follows [1].
Christiane Tretter – One of the best experts on this subject based on the ideXlab platform.

Bounds on the spectrum and reducing subspaces of a JselfAdjoint Operator
Indiana University Mathematics Journal, 2010CoAuthors: Sergio Albeverio, Alexander K. Motovilov, Christiane TretterAbstract:Given a selfAdjoint involution J on a Hilbert space H, we consider a JselfAdjoint Operator L=A+V on H where A is a possibly unbounded selfAdjoint Operator commuting with J and V a bounded JselfAdjoint Operator anticommuting with J. We establish optimal estimates on the position of the spectrum of L with respect to the spectrum of A and we obtain norm bounds on the Operator angles between maximal uniformly definite reducing subspaces of the unperturbed Operator A and the perturbed Operator L. All the bounds are given in terms of the norm of V and the distances between pairs of disjoint spectral sets associated with the Operator L and/or the Operator A. As an example, the quantum harmonic oscillator under a PTsymmetric perturbation is discussed. The sharp norm bounds obtained for the Operator angles generalize the celebrated DavisKahan trigonometric theorems to the case of JselfAdjoint perturbations.

the virozub matsaev condition and spectrum of definite type for self Adjoint Operator functions
Complex Analysis and Operator Theory, 2008CoAuthors: Matthias Langer, Heinz Langer, Alexander Markus, Christiane TretterAbstract:We establish sufficient conditions for the socalled Virozub–Matsaev condition for twice continuously differentiable selfAdjoint Operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to selfAdjoint Operators in Krein spaces and to quadratic Operator polynomials are given.

The Virozub–Matsaev Condition and Spectrum of Definite Type for SelfAdjoint Operator Functions
Complex Analysis and Operator Theory, 2007CoAuthors: Matthias Langer, Heinz Langer, Alexander Markus, Christiane TretterAbstract:We establish sufficient conditions for the socalled Virozub–Matsaev condition for twice continuously differentiable selfAdjoint Operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to selfAdjoint Operators in Krein spaces and to quadratic Operator polynomials are given.
Alexander Markus – One of the best experts on this subject based on the ideXlab platform.

the virozub matsaev condition and spectrum of definite type for self Adjoint Operator functions
Complex Analysis and Operator Theory, 2008CoAuthors: Matthias Langer, Heinz Langer, Alexander Markus, Christiane TretterAbstract:We establish sufficient conditions for the socalled Virozub–Matsaev condition for twice continuously differentiable selfAdjoint Operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to selfAdjoint Operators in Krein spaces and to quadratic Operator polynomials are given.

The Virozub–Matsaev Condition and Spectrum of Definite Type for SelfAdjoint Operator Functions
Complex Analysis and Operator Theory, 2007CoAuthors: Matthias Langer, Heinz Langer, Alexander Markus, Christiane TretterAbstract:We establish sufficient conditions for the socalled Virozub–Matsaev condition for twice continuously differentiable selfAdjoint Operator functions. This condition is closely related to the existence of a local spectral function and to the notion of positive type spectrum. Applications to selfAdjoint Operators in Krein spaces and to quadratic Operator polynomials are given.

self Adjoint analytic Operator functions and their local spectral function
Journal of Functional Analysis, 2006CoAuthors: Heinz Langer, Alexander Markus, Vladimir MatsaevAbstract:For a selfAdjoint analytic Operator function A(λ), which satisfies on some interval Δ of the real axis the Virozub–Matsaev condition, a local spectral function Q on Δ, the values of which are nonnegative Operators, is introduced and studied. In the particular case that A(λ)=λI−A with a selfAdjoint Operator A, it coincides with the orthogonal spectral function of A. An essential tool is a linearization of A(λ) by means of a selfAdjoint Operator in some Krein space and the local spectral function of this linearization. The main results of the paper concern properties of the range of Q(Δ) and the description of a natural complement of this range.