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 1930
... complex plane which contains the void set and the whole plane , in short , if Σ is a field of sets in the complex plane , then a spectral measure E on Σ is called a resolution of the identity ( or a spectral resolution ) for the ...
... complex plane which contains the void set and the whole plane , in short , if Σ is a field of sets in the complex plane , then a spectral measure E on Σ is called a resolution of the identity ( or a spectral resolution ) for the ...
Page 1935
... complex plane , σ ( E ( 81 ) x ) is void . By the preceding corollary , then E ( 81 ) x = 0. Let S be an increasing ... complex numbers is a closed linear manifold in X. 7 COROLLARY . Let T be a spectral operator and A a bounded linear ...
... complex plane , σ ( E ( 81 ) x ) is void . By the preceding corollary , then E ( 81 ) x = 0. Let S be an increasing ... complex numbers is a closed linear manifold in X. 7 COROLLARY . Let T be a spectral operator and A a bounded linear ...
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