Linear Operators: Spectral operators |
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Page 1917
... perturbed operator T and its perturbation T ' = TP , that is , to show the existence of an operator U such that - UTU 1 T ' . = This equation may be recast to permit the application of perturbation methods ; the whole approach has the ...
... perturbed operator T and its perturbation T ' = TP , that is , to show the existence of an operator U such that - UTU 1 T ' . = This equation may be recast to permit the application of perturbation methods ; the whole approach has the ...
Page 2510
... perturbation theory . A lively and enlightening survey of spectral perturbation theory from the hand of Friedrichs himself is available to us in K. O. Friedrichs [ 17 ] . Friedrichs ' monograph contains , among other things , an ...
... perturbation theory . A lively and enlightening survey of spectral perturbation theory from the hand of Friedrichs himself is available to us in K. O. Friedrichs [ 17 ] . Friedrichs ' monograph contains , among other things , an ...
Page 2542
... Perturbation of continuous spectra by trace class operators . Proc . Japan Acad . 33 , 260-264 ( 1957 ) . 10. On finite - dimensional perturbations of self - adjoint operators . J. Math . Soc . Japan 9 , 239–249 ( 1957 ) . 11 . 12 ...
... Perturbation of continuous spectra by trace class operators . Proc . Japan Acad . 33 , 260-264 ( 1957 ) . 10. On finite - dimensional perturbations of self - adjoint operators . J. Math . Soc . Japan 9 , 239–249 ( 1957 ) . 11 . 12 ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero