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 2299
... sufficiently large and for μ in C1 , we have | R ( μ ; T + P ) — R ( μ ; T ) | = | B ( μ ) — R ( μ ; T ) | since for sufficiently large n , 1 ≤ 2M dñ1 Ï ( [ \ n ] + d „ ) TM o d „ TM ( 2M | A | ) TM m = 1 ≤ 8M2 | A | d7 2 ( | λn ] + ...
... sufficiently large and for μ in C1 , we have | R ( μ ; T + P ) — R ( μ ; T ) | = | B ( μ ) — R ( μ ; T ) | since for sufficiently large n , 1 ≤ 2M dñ1 Ï ( [ \ n ] + d „ ) TM o d „ TM ( 2M | A | ) TM m = 1 ≤ 8M2 | A | d7 2 ( | λn ] + ...
Page 2360
... sufficiently large . From this it will then follow as above that the function f ( μ ) R ( μ ; TP ) f is uniformly ... sufficiently large , so that the theorem will be proved . i = Let μ be in V. To show that | TR ( μ ; T ) A | ≤ 1 , for ...
... sufficiently large . From this it will then follow as above that the function f ( μ ) R ( μ ; TP ) f is uniformly ... sufficiently large , so that the theorem will be proved . i = Let μ be in V. To show that | TR ( μ ; T ) A | ≤ 1 , for ...
Page 2394
... sufficiently small μ ɛ P + , such that σ and os are continuous in t and μ for 0 ≤t < ∞ and μ sufficiently small , and such that σz ( t , μ ) ~ e - itu ; ~ e ~ -iμe - itu ; o's ( t , μ ) ( μ ) ‡ 0 , | μ | as t → ∞ , for all μe P + ...
... sufficiently small μ ɛ P + , such that σ and os are continuous in t and μ for 0 ≤t < ∞ and μ sufficiently small , and such that σz ( t , μ ) ~ e - itu ; ~ e ~ -iμe - itu ; o's ( t , μ ) ( μ ) ‡ 0 , | μ | as t → ∞ , for all μe P + ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
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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 invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian 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