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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Results 1-3 of 67
Page 2149
... Theorem 3.13 the spectral measure E * of the preceding lemma may be extended from ( T ) to a spectral measure defined on M ( T ) . Then , as in the proof of Theorem 5 , it may be shown that σ ( T | E ( S ) X ) ≤ d for each 8 in M ( T ) ...
... Theorem 3.13 the spectral measure E * of the preceding lemma may be extended from ( T ) to a spectral measure defined on M ( T ) . Then , as in the proof of Theorem 5 , it may be shown that σ ( T | E ( S ) X ) ≤ d for each 8 in M ( T ) ...
Page 2162
... Lemma 4 , it has properties ( A ) and ( C ) . Thus , in view of Theorem 4.5 , to prove the present theorem it ... preceding theorem hold . PROOF . The proof is the same as that of the preceding theorem except that Theorem 4.7 is used ...
... Lemma 4 , it has properties ( A ) and ( C ) . Thus , in view of Theorem 4.5 , to prove the present theorem it ... preceding theorem hold . PROOF . The proof is the same as that of the preceding theorem except that Theorem 4.7 is used ...
Page 2396
... Lemma 1 ( cf. the para- graph following formula ( 14 ) ) that lim f ( t ) = 0 , uniformly for 0≤t < ∞o . 141 + 00 KEP + Hence , by formula ( 24 ) of the proof of Lemma 3 , Ĵu ( t ) ~ e - itu ; Î'u ( t ) = — iμe - ituƒ „ ( t ) + eituƒ ...
... Lemma 1 ( cf. the para- graph following formula ( 14 ) ) that lim f ( t ) = 0 , uniformly for 0≤t < ∞o . 141 + 00 KEP + Hence , by formula ( 24 ) of the proof of Lemma 3 , Ĵu ( t ) ~ e - itu ; Î'u ( t ) = — iμe - ituƒ „ ( t ) + eituƒ ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra 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 denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem 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