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 2082
... exercise , let x , xo , and σo be chosen so that x * E ( σ 。) x 。# 0 and let g be the Radon - Nikodým deriva- tive of x * E ( · ) x 。 with respect to μ . There is a subset σ of σ on which g is bounded away from zero and we let 1 / g ...
... exercise , let x , xo , and σo be chosen so that x * E ( σ 。) x 。# 0 and let g be the Radon - Nikodým deriva- tive of x * E ( · ) x 。 with respect to μ . There is a subset σ of σ on which g is bounded away from zero and we let 1 / g ...
Page 2172
... exercise and let o in ( l∞ ) * be a Banach limit as in Exercise II.4.22 . Let A be defined on l by Ax = A ( §1 , §2 , §3 , . . . ) = ( x ( x ) , 0 , 0 , ... ) . Show that A2 = 0 and that ( Tx ) = p ( x ) and ATTA . However , if σ = { 1 } ...
... exercise and let o in ( l∞ ) * be a Banach limit as in Exercise II.4.22 . Let A be defined on l by Ax = A ( §1 , §2 , §3 , . . . ) = ( x ( x ) , 0 , 0 , ... ) . Show that A2 = 0 and that ( Tx ) = p ( x ) and ATTA . However , if σ = { 1 } ...
Page 2489
... Exercise 17. ) 1 t → ∞ t ( a ) Show that the limit W + w = lim Uw exists , and that there exist operators A , B of ... Exercise 17. ) ( c ) ( Wave operator invariance theorem ) Show XX.5.19 2489 EXERCISES.
... Exercise 17. ) 1 t → ∞ t ( a ) Show that the limit W + w = lim Uw exists , and that there exist operators A , B of ... Exercise 17. ) ( c ) ( Wave operator invariance theorem ) Show XX.5.19 2489 EXERCISES.
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