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 M 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 M 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 ( ; T ) x with έ in p ( T ) . If σ is a closed set of complex numbers , the symbol M ( o ) will denote the ...
... 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 ( ; T ) x with έ in p ( T ) . If σ is a closed set of complex numbers , the symbol M ( o ) will denote the ...
Page 2188
... complex B - space X which is defined and countably additive on a σ - field Σ of subsets of a set △ and let g be a bounded Borel measurable function defined on the complex plane . Then √ g ( f ( x ) ) E ( dX ) = √ , 9 ( μ ) E ( ƒ − 1 ...
... complex B - space X which is defined and countably additive on a σ - field Σ of subsets of a set △ and let g be a bounded Borel measurable function defined on the complex plane . Then √ g ( f ( x ) ) E ( dX ) = √ , 9 ( μ ) E ( ƒ − 1 ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra 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 denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero