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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Results 1-3 of 64
Page 1979
... corresponding operator A = √ ¿ ( s ) e ( ds ) has its restrictions Ak | Ek Ho = Á | Eμ Ñ3 , and Âμ | ( I —- E ) = 0 , both spectral operators . Hence Theorem 3.10 shows that A is a spectral operator . Now since → it follows that e ...
... corresponding operator A = √ ¿ ( s ) e ( ds ) has its restrictions Ak | Ek Ho = Á | Eμ Ñ3 , and Âμ | ( I —- E ) = 0 , both spectral operators . Hence Theorem 3.10 shows that A is a spectral operator . Now since → it follows that e ...
Page 2292
... corresponding to the eigenvalue λ 。. If E ( λ 。; T ) = E ( λ ) is the idempotent function of T corresponding to the analytic function which is one near λo and zero elsewhere near the spectrum of T and near infinity , then E ( λ ...
... corresponding to the eigenvalue λ 。. If E ( λ 。; T ) = E ( λ ) is the idempotent function of T corresponding to the analytic function which is one near λo and zero elsewhere near the spectrum of T and near infinity , then E ( λ ...
Page 2305
... corresponding to these eigen- values is one - dimensional . It follows immediately from Corollary 9 that L + B is a ... corresponding eigenfunctions ( the corresponding projections having one- dimensional ranges ) are e2nin , n = 0 , 1 ...
... corresponding to these eigen- values is one - dimensional . It follows immediately from Corollary 9 that L + B is a ... corresponding eigenfunctions ( the corresponding projections having one- dimensional ranges ) are e2nin , n = 0 , 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