Linear Operators: Spectral operators |
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Page 2169
... bounded Borel functions , note that for a fixed continuous function g the set of all bounded Borel functions ƒ for which ( vi ) ( fg ) ( T ) = ƒ ( T ) g ( T ) , includes all continuous functions . Furthermore , if the equation ( vi ) ...
... bounded Borel functions , note that for a fixed continuous function g the set of all bounded Borel functions ƒ for which ( vi ) ( fg ) ( T ) = ƒ ( T ) g ( T ) , includes all continuous functions . Furthermore , if the equation ( vi ) ...
Page 2188
... bounded Borel measurable functions g for which √ , 9 ( μ ) E ( dμ ) = √ g ( f ( x ) ) E ( dx ) f ( 4 ) is clearly linear and closed in the set of all bounded Borel functions . Since this set contains every characteristic function of a ...
... bounded Borel measurable functions g for which √ , 9 ( μ ) E ( dμ ) = √ g ( f ( x ) ) E ( dx ) f ( 4 ) is clearly linear and closed in the set of all bounded Borel functions . Since this set contains every characteristic function of a ...
Page 2233
... bounded Borel sets whose closures are in U , by the equation Qox = f ( TE ( e ) X ) x , x = E ( e ) X . Now , using the machinery established in Lemma 6 , ƒ ( T ) may be defined as follows . = 8 DEFINITION . Let T be a spectral operator ...
... bounded Borel sets whose closures are in U , by the equation Qox = f ( TE ( e ) X ) x , x = E ( e ) X . Now , using the machinery established in Lemma 6 , ƒ ( T ) may be defined as follows . = 8 DEFINITION . Let T be a spectral operator ...
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