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 2025
... gives - ( 40 ) - | λ = √x ( 8 ) | ′′ 1 = √ ( 8 ) | ≤ M n = 1 , 2 , " .... ( λ - w ) n - ω Since ( √ ( 8 ) ) > w we may fix À so large that | λ — √x , ( s ) | < λw and thus the fraction appearing in ( 40 ) approaches zero as n ...
... gives - ( 40 ) - | λ = √x ( 8 ) | ′′ 1 = √ ( 8 ) | ≤ M n = 1 , 2 , " .... ( λ - w ) n - ω Since ( √ ( 8 ) ) > w we may fix À so large that | λ — √x , ( s ) | < λw and thus the fraction appearing in ( 40 ) approaches zero as n ...
Page 2031
... gives ( FT ̧ ) ( q ) = √ ( Fq ) ( s ) 4 ( s ) ds = [ __9 ( 8 ) ( F4 ) ( 8 ) ds = Trv ( 4 ) , RN RN : = Ø ΚΕΦ . Now is dense in H = L2 ( RN ) and thus there is for an arbitrary in Ha ≤ n → FØ 5 a sequence { n } with n in 5. Since F ...
... gives ( FT ̧ ) ( q ) = √ ( Fq ) ( s ) 4 ( s ) ds = [ __9 ( 8 ) ( F4 ) ( 8 ) ds = Trv ( 4 ) , RN RN : = Ø ΚΕΦ . Now is dense in H = L2 ( RN ) and thus there is for an arbitrary in Ha ≤ n → FØ 5 a sequence { n } with n in 5. Since F ...
Page 2065
... gives more by asserting that the inverse a - 1 is in A1 . 1 The basic notions underlying the proof of Wiener's theorem as it will be presented here are those to be found in I. M. Gelfand's theory of com- mutative normed rings , or B ...
... gives more by asserting that the inverse a - 1 is in A1 . 1 The basic notions underlying the proof of Wiener's theorem as it will be presented here are those to be found in I. M. Gelfand's theory of com- mutative normed rings , or B ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 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