Some spectral properties for operators acting on Rigged Hilbert spaces

2015 ◽  
pp. 389-397
Author(s):  
Salvatore Di Bella
Keyword(s):  
Hilbert Spaces ◽  
Spectral Properties ◽  
Rigged Hilbert Spaces

scholarly journals Operators in rigged Hilbert spaces: Some spectral properties

2014 ◽  
Vol 411 (2) ◽  
pp. 931-946 ◽  
Author(s):  
Giorgia Bellomonte ◽  
Salvatore Di Bella ◽  
Camillo Trapani
Keyword(s):  
Hilbert Spaces ◽  
Spectral Properties ◽  
Rigged Hilbert Spaces

scholarly journals Zernike functions, rigged Hilbert spaces, and potential applications

2019 ◽  
Vol 60 (8) ◽  
pp. 083508 ◽  
Author(s):  
E. Celeghini ◽  
M. Gadella ◽  
M. A. del Olmo
Keyword(s):  
Hilbert Spaces ◽  
Rigged Hilbert Spaces ◽  
Potential Applications

scholarly journals A Special Class of Infinite Dimensional Dirac Operators on the Abstract Boson-Fermion Fock Space

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Asao Arai
Keyword(s):  
Dirac Operator ◽  
Hilbert Spaces ◽  
Special Class ◽  
Spectral Properties ◽  
Fock Space ◽  
Dirac Operators ◽  
Fredholm Property ◽  
Perturbation Parameter ◽  
Coupling Constant ◽  
Infinite Dimensional

Spectral properties of a special class of infinite dimensional Dirac operatorsQ(α)on the abstract boson-fermion Fock spaceℱ(ℋ,𝒦)associated with the pair(ℋ,𝒦)of complex Hilbert spaces are investigated, whereα∈Cis a perturbation parameter (a coupling constant in the context of physics) and the unperturbed operatorQ(0)is taken to be a free infinite dimensional Dirac operator. A variety of the kernel ofQ(α)is shown. It is proved that there are cases where, for all sufficiently large|α|withα<0,Q(α)has infinitely many nonzero eigenvalues even ifQ(0)has no nonzero eigenvalues. Also Fredholm property ofQ(α)restricted to a subspace ofℱ(ℋ,𝒦)is discussed.

scholarly journals Riesz-Like Bases in Rigged Hilbert Spaces

2016 ◽  
Vol 35 (3) ◽  
pp. 243-265 ◽  
Author(s):  
Giorgia Bellomonte ◽  
Camillo Trapani
Keyword(s):  
Hilbert Spaces ◽  
Rigged Hilbert Spaces
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