Linear Operators, Part 2 |
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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 ) = ( F2q ) ( − s ) , which proves that FØ = 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 ) = ( F2q ) ( − s ) , which proves that FØ = Ø and thus that the ... established by 1986 XV.11.1 XV . SPECTRAL OPERATORS.
Page 2212
... establish the relation ( ix ) ƒz ( ^ ) = ƒy ( ^ λ ) , = λεσι σν · σy , for if z = E1x and w = Ey y To prove ( ix ) it may be assumed that σ it follows from ( vii ) that σ = σ , σ = σ and fw = Xofy . Thus if f2 ( A ) = fw ( ) on established ...
... establish the relation ( ix ) ƒz ( ^ ) = ƒy ( ^ λ ) , = λεσι σν · σy , for if z = E1x and w = Ey y To prove ( ix ) it may be assumed that σ it follows from ( vii ) that σ = σ , σ = σ and fw = Xofy . Thus if f2 ( A ) = fw ( ) on established ...
Page 2234
... established for bounded Borel sets with closures contained in U , f ( T | E ( e ) X ) x = lim f ( T | F ( en ) E ( e ) X ) F ( en ) x = - lim f ( TE ( ee ) X ) E ( en ) x ∞o + - น lim f ( T ) E ( en ) x . Since E ( en ) xx , and since ...
... established for bounded Borel sets with closures contained in U , f ( T | E ( e ) X ) x = lim f ( T | F ( en ) E ( e ) X ) F ( en ) x = - lim f ( TE ( ee ) X ) E ( en ) x ∞o + - น lim f ( T ) E ( en ) x . Since E ( en ) xx , and since ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero