Linear Operators: Spectral operators |
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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 q ( 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 q ( 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 equation ( viii ) fF1 = f1Xo ( F ) , Fe B. To prove this , let g = f1X ( 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 ) fF1 = f1Xo ( F ) , Fe B. To prove this , let g = f1X ( 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 ƒ ( T | E ( e ) X ) x = lim ƒ ( T | F ( en ) E ( e ) X ) F ( en ) x = = lim ƒ ( T | E ( een ) X ) E ( en ) x lim f ( T ) E ( en ) x . Since E ( en ) xx , and since ƒ ...
... established for bounded Borel sets with closures contained in U , n ƒ ( T | E ( e ) X ) x = lim ƒ ( T | F ( en ) E ( e ) X ) F ( en ) x = = lim ƒ ( T | E ( een ) X ) E ( en ) x lim f ( T ) E ( en ) x . Since E ( en ) xx , and since ƒ ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero