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 2322
... hypothesis . 1 Πι and REGULARITY HYPOTHESIS FOR EVEN ORDER CASE . The polynomials π2 are of order p . If Regularity Hypothesis 1 is satisfied , we may write 2322 XIX.4.1 XIX . PERTURBATIONS OF SPECTRAL OPERATORS.
... hypothesis . 1 Πι and REGULARITY HYPOTHESIS FOR EVEN ORDER CASE . The polynomials π2 are of order p . If Regularity Hypothesis 1 is satisfied , we may write 2322 XIX.4.1 XIX . PERTURBATIONS OF SPECTRAL OPERATORS.
Page 2401
... hypothesis ( b ) , to ( 4 ) Using hypothesis ( c ) , we may write this last equation as ( 5 ) ¤ ( B — √ ( B , A1 ) ) = q ( A1 ) . Now , by hypothesis , the map B → ↓ ( B , A1 ) of A → A has norm at most M2 ( M1 + M2 ) -1 . Thus , by ...
... hypothesis ( b ) , to ( 4 ) Using hypothesis ( c ) , we may write this last equation as ( 5 ) ¤ ( B — √ ( B , A1 ) ) = q ( A1 ) . Now , by hypothesis , the map B → ↓ ( B , A1 ) of A → A has norm at most M2 ( M1 + M2 ) -1 . Thus , by ...
Page 2449
... hypothesis , 6M2t1 ≤ 1 , we have n + 12t1 and our assertion follows . It also follows from ( 5 ) and hypotheses ( d ) and ( e ) that ( 7 ) ||| A ( n + 1 ) — A ( n ) ||| - ( n - 1 ) ≤ M2 ( || A || + ||| An − 1 ) ||| + ||| A1 ...
... hypothesis , 6M2t1 ≤ 1 , we have n + 12t1 and our assertion follows . It also follows from ( 5 ) and hypotheses ( d ) and ( e ) that ( 7 ) ||| A ( n + 1 ) — A ( n ) ||| - ( n - 1 ) ≤ M2 ( || A || + ||| An − 1 ) ||| + ||| A1 ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
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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