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 2084
... complex B - space X which satisfies the growth condition ( * ) in Theorem XV.6.7 , namely ( * ) | R ( § ; T , ) E ( 0 ) | ≤ K dist ( , ) m for § ō , | § | ≤ | T | + 1. If k is a natural number then there exists a constant Mx such that ...
... complex B - space X which satisfies the growth condition ( * ) in Theorem XV.6.7 , namely ( * ) | R ( § ; T , ) E ( 0 ) | ≤ K dist ( , ) m for § ō , | § | ≤ | T | + 1. If k is a natural number then there exists a constant Mx such that ...
Page 2171
... complex B - space X. For each x in x the symbol [ x ] will be used for the closed linear manifold determined by all the vectors R ( έ ; T ) x with έ in p ( T ) . If σ is a closed set of complex numbers , the symbol M ( o ) will denote ...
... complex B - space X. For each x in x the symbol [ x ] will be used for the closed linear manifold determined by all the vectors R ( έ ; T ) x with έ in p ( T ) . If σ is a closed set of complex numbers , the symbol M ( o ) will denote ...
Page 2188
... complex B - space X which is defined and countably additive on a o - field Σ of subsets of a set Д and let g be a bounded Borel measurable function defined on the complex plane . Then ↓ g ( f ( x ) ) E ( d ) ) = √ , 9 ( μ ) E ( ƒ − 1 ...
... complex B - space X which is defined and countably additive on a o - field Σ of subsets of a set Д and let g be a bounded Borel measurable function defined on the complex plane . Then ↓ g ( f ( x ) ) E ( d ) ) = √ , 9 ( μ ) E ( ƒ − 1 ...
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