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 2141
... assume without loss of generality that σ is void . Since E ( om ) = E ( 0m0 ( T ) ) , by the preceding lemma , we may also assume that om o ( T ) . ≤ Suppose that our assertion is false , so that there is a p > 0 and a vector x such ...
... assume without loss of generality that σ is void . Since E ( om ) = E ( 0m0 ( T ) ) , by the preceding lemma , we may also assume that om o ( T ) . ≤ Suppose that our assertion is false , so that there is a p > 0 and a vector x such ...
Page 2212
... assume , in the proof of ( ix ) , that I on σ2 = Since A ( xy ) = Ax- Ay it follows that T ( fx − y ) ( x − y ) ... assume that the functions f , and f , are not identically equal and one of them , say fr , differs from both fy and f ...
... assume , in the proof of ( ix ) , that I on σ2 = Since A ( xy ) = Ax- Ay it follows that T ( fx − y ) ( x − y ) ... assume that the functions f , and f , are not identically equal and one of them , say fr , differs from both fy and f ...
Page 2250
... assuming that E ( ƒ - 1 ( q ' ) ) = I. This amounts to taking U = q ' , that is , to assuming that , even if ƒ is analytic at infinity , it does not assume its value at infinity anywhere in f - 1 ( U ) . - Now let e , be an increasing ...
... assuming that E ( ƒ - 1 ( q ' ) ) = I. This amounts to taking U = q ' , that is , to assuming that , even if ƒ is analytic at infinity , it does not assume its value at infinity anywhere in f - 1 ( U ) . - Now let e , be an increasing ...
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