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On the Normality of the Unbounded Product of Two Normal Operators

100%

Mortad M. H.

Concrete Operators

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2013

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tom 1

11-18

EN

Let A and B be two -non necessarily bounded- normal operators. We give new conditions making their product normal. We also generalize a result by Deutsch et al on normal products of matrices.

2

Approximation and asymptotics of eigenvalues of unbounded self-adjoint Jacobi matrices acting in l 2 by the use of finite submatrices

76%

Malejki M.

Open Mathematics

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2010

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tom 8

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nr 1

114-128

EN

We consider the problem of approximation of eigenvalues of a self-adjoint operator J defined by a Jacobi matrix in the Hilbert space l 2(ℕ) by eigenvalues of principal finite submatrices of an infinite Jacobi matrix that defines this operator. We assume the operator J is bounded from below with compact resolvent. In our research we estimate the asymptotics (with n → ∞) of the joint error of approximation for the eigenvalues, numbered from 1 to N; of J by the eigenvalues of the finite submatrix J n of order n × n; where N = max{k ∈ ℕ: k ≤ rn} and r ∈ (0; 1) is arbitrary chosen. We apply this result to obtain an asymptotics for the eigenvalues of J. The method applied in this research is based on Volkmer’s results included in [23].

3

Unbounded Hermitian operators and relative reproducing kernel Hilbert space

52%

Jorgensen P.

Open Mathematics

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2010

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tom 8

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nr 3

569-596

EN

We study unbounded Hermitian operators with dense domain in Hilbert space. As is known, the obstruction for a Hermitian operator to be selfadjoint or to have selfadjoint extensions is measured by a pair of deficiency indices, and associated deficiency spaces; but in practical problems, the direct computation of these indices can be difficult. Instead, in this paper we identify additional structures that throw light on the problem. We will attack the problem of computing deficiency spaces for a single Hermitian operator with dense domain in a Hilbert space which occurs in a duality relation with a second Hermitian operator, often in the same Hilbert space.

Ograniczanie wyników

2 Open Mathematics

1 Concrete Operators

1 Jorgensen P.

1 Malejki M.

1 Mortad M. H.

1 2012

2 2010

On the Normality of the Unbounded Product of Two Normal Operators

Approximation and asymptotics of eigenvalues of unbounded self-adjoint Jacobi matrices acting in l 2 by the use of finite submatrices

Unbounded Hermitian operators and relative reproducing kernel Hilbert space