Linear Operators: Spectral operators |
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Page 2299
... sufficiently large and for μ in Cn , we have | R ( μ ; T + P ) — R ( μ ; T ) | = | B ( μ ) — R ( μ ; T ) | since for sufficiently large n , 00 1 ≤ 2M dñ1 Σ ( [ ^ n | + d „ ) TM o d „ m ( 2M | A | ) m m = 1 ≤ 8M2 | A | d7 2 ( | λn ] + ...
... sufficiently large and for μ in Cn , we have | R ( μ ; T + P ) — R ( μ ; T ) | = | B ( μ ) — R ( μ ; T ) | since for sufficiently large n , 00 1 ≤ 2M dñ1 Σ ( [ ^ n | + d „ ) TM o d „ m ( 2M | A | ) m m = 1 ≤ 8M2 | A | d7 2 ( | λn ] + ...
Page 2300
... sufficiently large p . Since E is a count- ably additive spectral resolution , we have E ( μ ; T + P ) ( I — E2 ) = 0 if μ is not one of the points μn , n ≥ K. It follows from Lemma 3 that o ( T + P ) consists of the union of the ...
... sufficiently large p . Since E is a count- ably additive spectral resolution , we have E ( μ ; T + P ) ( I — E2 ) = 0 if μ is not one of the points μn , n ≥ K. It follows from Lemma 3 that o ( T + P ) consists of the union of the ...
Page 2360
... sufficiently large . From this it will then follow as above that the function ƒ ( μ ) Ru ; TP ) f is uniformly ... sufficiently large , so that the theorem will be proved . i = Let μ be in V. To show that | T'R ( μ ; T ) A | ≤ , for i ...
... sufficiently large . From this it will then follow as above that the function ƒ ( μ ) Ru ; TP ) f is uniformly ... sufficiently large , so that the theorem will be proved . i = Let μ be in V. To show that | T'R ( μ ; T ) A | ≤ , for i ...
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