The Krein string and characteristic functions of non-self-adjoint operators.

Kostenko, A.S.

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$D$ -symmetric operators: comments and some open problems.

Mecheri, Salah (2008)

Banach Journal of Mathematical Analysis [electronic only]

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A characterization of formally symmetric unbounded operators.

Jocić, Danko (1989)

Publications de l'Institut Mathématique. Nouvelle Série

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Generalized D-Symmetric Operators I

Bouali, S., Ech-chad, M. (2008)

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2000 Mathematics Subject Classification: Primary: 47B47, 47B10; secondary 47A30. Let H be an infinite-dimensional complex Hilbert space and let A, B ∈ L(H), where L(H) is the algebra of operators on H into itself. Let δAB: L(H) → L(H) denote the generalized derivation δAB(X) = AX − XB. This note will initiate a study on the class of pairs (A,B) such that [‾(R(δAB))] = [‾(R(δB*A*))]; i.e. [‾(R(δAB))] is self-adjoint.

Generalized derivations and $C^{*}$ -algebras.

Mecheri, Salah (2009)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Extensions of symmetric operators I: The inner characteristic function case

R.T.W. Martin (2015)

Concrete Operators

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Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θB by constructing a bijection...

Extensions of two classic kinds of Wachs space operators

A. Torgašev (1976)

Matematički Vesnik

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Backward extensions of hyperexpansive operators

Zenon J. Jabłoński, Il Bong Jung, Jan Stochel (2006)

Studia Mathematica

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The concept of k-step full backward extension for subnormal operators is adapted to the context of completely hyperexpansive operators. The question of existence of k-step full backward extension is solved within this class of operators with the help of an operator version of the Levy-Khinchin formula. Some new phenomena in comparison with subnormal operators are found and related classes of operators are discussed as well.

Generalized resolvents and spectrum for a certain class of perturbed symmetric operators.

Hebbeche, A. (2005)

Journal of Applied Mathematics

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On the solution of Nevanlinna Pick problem with selfadjoint extensions of symmetric linear relations in Hilbert space.

El-Sabbagh, A.A. (1997)

International Journal of Mathematics and Mathematical Sciences

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A study of an operator arising in the theory of circular plates

Leopold Herrmann (1988)

Aplikace matematiky

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The operator $L_{0} : D_{L_{0}} \subset H \to H$ , $L_{0} u = \frac{1}{r} \frac{d}{d r} \{r \frac{d}{d r} [\frac{1}{r} \frac{d}{d r} (r \frac{d u}{d r})]\}$ , $D_{L_{0}} = {u \in C^{4} ([0, R]), u^{'} (0) = u^{''''} (0) = 0, u (R) = u^{'} (R) = 0}$ , $H = L_{2, r} (0, R)$ is shown to be essentially self-adjoint, positive definite with a compact resolvent. The conditions on $L_{0}$ (in fact, on a general symmetric operator) are given so as to justify the application of the Fourier method for solving the problems of the types $L_{0} u = g$ and $u_{t t} + L_{0} u = g$ , respectively.

Backward Aluthge iterates of a hyponormal operator and scalar extensions

C. Benhida, E. H. Zerouali (2009)

Studia Mathematica

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Let R and S be two operators on a Hilbert space. We discuss the link between the subscalarity of RS and SR. As an application, we show that backward Aluthge iterates of hyponormal operators and p-quasihyponormal operators are subscalar.