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 2410
... constant ɛ ε ( p , D ) depending only on p and D such that if || A || < ε ( p , D ) it follows that the operator T + q ( A ) is similar to the operator T and is therefore a spectral operator of scalar type . The following theorem ...
... constant ɛ ε ( p , D ) depending only on p and D such that if || A || < ε ( p , D ) it follows that the operator T + q ( A ) is similar to the operator T and is therefore a spectral operator of scalar type . The following theorem ...
Page 2439
... constant c 。 such that sin co | sin ( 0/2 ) | for 0 ≤ | 0 | ≤ π / 2 , formula ( 30 ) follows at once . Using ( 27 ) , ( 30 ) , and ( 31 ) , we see that there exists a finite constant M ' independent of ε such that ( 33 ) | V ( rw — r ...
... constant c 。 such that sin co | sin ( 0/2 ) | for 0 ≤ | 0 | ≤ π / 2 , formula ( 30 ) follows at once . Using ( 27 ) , ( 30 ) , and ( 31 ) , we see that there exists a finite constant M ' independent of ε such that ( 33 ) | V ( rw — r ...
Page 2441
... constant c ' such that I ( a ) | ≤ c ' ( 1 + | a | ) -n + 1 . Using this inequality and using ( 37 ) , we see that there exists a finite constant M " independent of ɛ such that ε ( 43 ) | V1 ( r , r ' ) | + av 4 др av1 4 Ꭷ 2 Ꮩ . 4 ...
... constant c ' such that I ( a ) | ≤ c ' ( 1 + | a | ) -n + 1 . Using this inequality and using ( 37 ) , we see that there exists a finite constant M " independent of ɛ such that ε ( 43 ) | V1 ( r , r ' ) | + av 4 др av1 4 Ꭷ 2 Ꮩ . 4 ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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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