On the product of self-adjoint operators.

Rehder, Wulf

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J. van Casteren, Seymour Goldberg (1970)

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A perturbation characterization of compactness of self-adjoint operators

Heydar Radjavi, Ping-Kwan Tam, Kok-Keong Tan (2003)

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A characterization of compactness of a given self-adjoint bounded operator A on a separable infinite-dimensional Hilbert space is established in terms of the spectrum of perturbations. An example is presented to show that without separability, the perturbation condition, which is always necessary, is not sufficient. For non-separable spaces, another condition on the self-adjoint operator A, which is necessary and sufficient for the perturbation, is given.

On Commuting Unbounded Self-Adjoint Operators. III.

Konrad Schmüdgen (1986)

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Exponentials of normal operators and commutativity of operators: a new approach

Mohammed Hichem Mortad (2011)

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We present a new approach to the question of when the commutativity of operator exponentials implies that of the operators. This is proved in the setting of bounded normal operators on a complex Hilbert space. The proofs are based on some results on similarities by Berberian and Embry as well as the celebrated Fuglede theorem.

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

Leopold Herrmann (1988)

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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.

Conditions for two self-adjoint operators to commute or to satisfy the Weyl relation.

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Norm inequality for the class of self-adjoint absolute value generalized derivations.

Jocić, Danko R. (1997)

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Fuglede-Putnam theorem for class A operators

Salah Mecheri (2015)

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Let A ∈ B(H) and B ∈ B(K). We say that A and B satisfy the Fuglede-Putnam theorem if AX = XB for some X ∈ B(K,H) implies A*X = XB*. Patel et al. (2006) showed that the Fuglede-Putnam theorem holds for class A(s,t) operators with s + t < 1 and they mentioned that the case s = t = 1 is still an open problem. In the present article we give a partial positive answer to this problem. We show that if A ∈ B(H) is a class A operator with reducing kernel and B* ∈ B(K) is a class 𝓨 operator,...

On a Weyl-von Neumann type theorem for antilinear self-adjoint operators

Santtu Ruotsalainen (2012)

Studia Mathematica

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Antilinear operators on a complex Hilbert space arise in various contexts in mathematical physics. In this paper, an analogue of the Weyl-von Neumann theorem for antilinear self-adjoint operators is proved, i.e. that an antilinear self-adjoint operator is the sum of a diagonalizable operator and of a compact operator with arbitrarily small Schatten p-norm. On the way, we discuss conjugations and their properties. A spectral integral representation for antilinear self-adjoint operators...