Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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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 ) E1 ( dμ ) = { _g ( f ( x ) ) E ( dA ) 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 ) E1 ( dμ ) = { _g ( f ( x ) ) E ( dA ) 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 = ƒ ( T | E ( e ) X ) x , x = E ( e ) X . Now , using the machinery established in Lemma 6 , f ( T ) may be defined as follows . = 8 DEFINITION . Let T be a spectral ...
... bounded Borel sets whose closures are in U , by the equation Qox = ƒ ( T | E ( e ) X ) x , x = E ( e ) X . Now , using the machinery established in Lemma 6 , f ( T ) may be defined as follows . = 8 DEFINITION . Let T be a spectral ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero