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 2331
... uniformly bounded for μ in Co and m ≥1 ( by formula ( 4 ) ) and that ok ( 1 − y , μ + 2πm ) = σ¿ ( 1 — y , μ ) σ , ( 1 — y , 2πm ) ( by this same formula ) , to establish the following two separate assertions . ( a ) For 0 ≤k , j < n ...
... uniformly bounded for μ in Co and m ≥1 ( by formula ( 4 ) ) and that ok ( 1 − y , μ + 2πm ) = σ¿ ( 1 — y , μ ) σ , ( 1 — y , 2πm ) ( by this same formula ) , to establish the following two separate assertions . ( a ) For 0 ≤k , j < n ...
Page 2341
... uniformly bounded . This follows from ( 58 ) by an argument using Lemma 7 , which is similar to the corres- ponding ... uniformly bounded . Hence it is seen that : the collection of all finite sums of projections E ( X ; T ) , with λ in ...
... uniformly bounded . This follows from ( 58 ) by an argument using Lemma 7 , which is similar to the corres- ponding ... uniformly bounded . Hence it is seen that : the collection of all finite sums of projections E ( X ; T ) , with λ in ...
Page 2361
... bounded domains covering the whole complex plane , and suppose that lim → ∞ minze v1 | 2 | oo . Let V , be the ... uniformly bounded for each ƒe S. ( ( T + P ) * ) . However , in the course of the proof of Theorem 6 it was established ...
... bounded domains covering the whole complex plane , and suppose that lim → ∞ minze v1 | 2 | oo . Let V , be the ... uniformly bounded for each ƒe S. ( ( T + P ) * ) . However , in the course of the proof of Theorem 6 it was established ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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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