Vectorial Hankel operators, commutators and related operators of the Schatten-von Neumann class .

1982 ◽  
Vol 5 (1) ◽  
pp. 244-272 ◽  
Author(s):  
Vladimir V. Peller
Keyword(s):  
Hankel Operators ◽  
Von Neumann ◽  
Neumann Class

Local Price uncertainty principle and time-frequency localization operators for the Hankel–Stockwell transform

2020 ◽  
Vol 18 (06) ◽  
pp. 2050050
Author(s):  
Nadia Ben Hamadi ◽  
Zineb Hafirassou
Keyword(s):  
Uncertainty Principle ◽  
Price Uncertainty ◽  
Localization Operators ◽  
Von Neumann ◽  
Time Frequency ◽  
Neumann Class ◽  
Time Frequency Localization ◽  
Stockwell Transform

For the Hankel–Stockwell transform, the Price uncertainty principle is proved, we define the Localization operators and we study their boundedness and compactness. We also show that these operators belong to the so-called Schatten–von Neumann class.

Entropy of dynamical systems and perturbations of operators

1991 ◽  
Vol 11 (4) ◽  
pp. 779-786 ◽  
Author(s):  
Dan Voiculescu
Keyword(s):  
Hilbert Space ◽  
Dynamical Systems ◽  
Lower Bound ◽  
Hausdorff Measure ◽  
Spectral Measure ◽  
Von Neumann ◽  
Dimensional Hausdorff Measure ◽  
Hilbert Space Operators ◽  
Neumann Class ◽  
Adjoint Operators

In the papers [9, 10, 3, 11] on perturbations of Hilbert space operators, we studied an invariant (τ) where is a normed ideal of compact operators and τ a family of operators. The size of an ideal for which (τ) vanishes or does not vanish is an upper, respectively lower, bound for a kind of dimension of τ. In the case of systems of commuting self-adjoint operators τ, the results of [9,3] relate (τ) with (an ideal slightly smaller than the Schatten von Neumann class ) to the way the spectral measure of τ compares to p-dimensional Hausdorff measure.

scholarly journals On One Method of Studying Spectral Properties of Non-selfadjoint Operators

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Maksim V. Kukushkin
Keyword(s):  
Spectral Properties ◽  
Root Vector ◽  
Vector System ◽  
Real Component ◽  
Von Neumann ◽  
The Real ◽  
Selfadjoint Operators ◽  
Neumann Class ◽  
Nonselfadjoint Operator

In this paper, we explore a certain class of Non-selfadjoint operators acting on a complex separable Hilbert space. We consider a perturbation of a nonselfadjoint operator by an operator that is also nonselfadjoint. Our consideration is based on known spectral properties of the real component of a nonselfadjoint compact operator. Using a technique of the sesquilinear forms theory, we establish the compactness property of the resolvent and obtain the asymptotic equivalence between the real component of the resolvent and the resolvent of the real component for some class of nonselfadjoint operators. We obtain a classification of nonselfadjoint operators in accordance with belonging their resolvent to the Schatten-von Neumann class and formulate a sufficient condition of completeness of the root vector system. Finally, we obtain an asymptotic formula for the eigenvalues.

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