Linear Operators: Spectral operators |
From inside the book
Results 1-3 of 62
Page 1986
... establish the inversion formula ( 5 ) . Once this is done , it will follow that F is one - to - one on Ø and that p ( s ) = ( F2p ) ( − s ) , which proves that F = Ø and thus that the ... established by 1986 XV.11.1 XV . SPECTRAL OPERATORS.
... establish the inversion formula ( 5 ) . Once this is done , it will follow that F is one - to - one on Ø and that p ( s ) = ( F2p ) ( − s ) , which proves that F = Ø and thus that the ... established by 1986 XV.11.1 XV . SPECTRAL OPERATORS.
Page 2212
... establish the equation ( viii ) fFx = ft Xo ( F ) , FEB . To prove this , let g = fr Xo ( F ) so that , using ( vii ) , we ... established . Hence we may and shall assume , in the proof of ( ix ) , that = Since A ( x − y ) = Ax — Ay it ...
... establish the equation ( viii ) fFx = ft Xo ( F ) , FEB . To prove this , let g = fr Xo ( F ) so that , using ( vii ) , we ... established . Hence we may and shall assume , in the proof of ( ix ) , that = Since A ( x − y ) = Ax — Ay it ...
Page 2234
... established for bounded Borel sets with closures contained in U , n f ( T | E ( e ) X ) x = lim f ( T | F ( en ) E ( e ) X ) F ( en ) x = lim f ( T | E ( een ) X ) E ( en ) x n → ∞ = lim f ( T ) E ( en ) x . + น - Since E ( e ) xx ...
... established for bounded Borel sets with closures contained in U , n f ( T | E ( e ) X ) x = lim f ( T | F ( en ) E ( e ) X ) F ( en ) x = lim f ( T | E ( een ) X ) E ( en ) x n → ∞ = lim f ( T ) E ( en ) x . + น - Since E ( e ) xx ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
20 other sections not shown
Other editions - View all
Common terms and phrases
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