Linear Operators: Spectral operators |
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Page 1909
... theory forms an excellent introduction to the detailed study of the much more refined and complete theory of self adjoint operators in Hilbert space . It soon became evident , however , that the natural limitations imposed by size ...
... theory forms an excellent introduction to the detailed study of the much more refined and complete theory of self adjoint operators in Hilbert space . It soon became evident , however , that the natural limitations imposed by size ...
Page 2112
... theory of type 3 if for arbitrary open sets G1 , ... , G2 which cover the complex plane , there exist closed linear subspaces M1 , ... , Mn which span X , are invariant under T , and such that o ( T | M1 ) ≤ Ğ1 , i = 1 , ... , n . ( iv ) ...
... theory of type 3 if for arbitrary open sets G1 , ... , G2 which cover the complex plane , there exist closed linear subspaces M1 , ... , Mn which span X , are invariant under T , and such that o ( T | M1 ) ≤ Ğ1 , i = 1 , ... , n . ( iv ) ...
Page 2510
... 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 especially ...
... 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 especially ...
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