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 66
Page 1962
... corresponding upper and lower case letters for corresponding elements . It is clear that the mapping A↔ ( a ,, ) is linear . It is , in fact , an algebraic isomorphism between the algebras B ( H ” ) and M , ( B ( H ) ) , for if A↔ ( a ...
... corresponding upper and lower case letters for corresponding elements . It is clear that the mapping A↔ ( a ,, ) is linear . It is , in fact , an algebraic isomorphism between the algebras B ( H ” ) and M , ( B ( H ) ) , for if A↔ ( a ...
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 λ and zero elsewhere near the spectrum of T and near infinity , then E ( o ) ...
... 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 λ and zero elsewhere near the spectrum of T and near infinity , then E ( o ) ...
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 e2лin , 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 e2лin , n = 0 , ± 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