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 2148
... consequently λ is in p ( T ) , which means that XI – T is a one - to - one map of E ( o ) X into all of itself . Since o do ( T ) , we have E ( σ ) ≥ E ( So ( T ) ) = E ( S ) and consequently E ( 8 ) X is an invariant subspace of E ( o ) ...
... consequently λ is in p ( T ) , which means that XI – T is a one - to - one map of E ( o ) X into all of itself . Since o do ( T ) , we have E ( σ ) ≥ E ( So ( T ) ) = E ( S ) and consequently E ( 8 ) X is an invariant subspace of E ( o ) ...
Page 2323
... Consequently , by factoring out a factor ( iμ ) " , the coefficients a ,, bp , c , of the terms of order p in the determinant N ( μ ) become the same as the coefficients a , b , c , in the determinant ( u ) = a , e " + b2 e ̄1 " + C2 of ...
... Consequently , by factoring out a factor ( iμ ) " , the coefficients a ,, bp , c , of the terms of order p in the determinant N ( μ ) become the same as the coefficients a , b , c , in the determinant ( u ) = a , e " + b2 e ̄1 " + C2 of ...
Page 2343
... Consequently , if we use Lagrange's rule to expand this 2v × 2v deter- minant by minors of order v , we find that the expansion contains only two non - vanishing terms . Thus our 2v × 2v determinant may be expressed as P1P2Q1Q2 , where ...
... Consequently , if we use Lagrange's rule to expand this 2v × 2v deter- minant by minors of order v , we find that the expansion contains only two non - vanishing terms . Thus our 2v × 2v determinant may be expressed as P1P2Q1Q2 , where ...
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