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 2010
... vanishes on Use 。。 σ ( Â ( s ) ) , and since q is continuous , it also vanishes on the closure of this set . Thus Corollary 9.9 shows that p vanishes on σ ( A ) , which means that = Ф 0 . To prove ( 76 ) it is seen from Theorem 9.3 ...
... vanishes on Use 。。 σ ( Â ( s ) ) , and since q is continuous , it also vanishes on the closure of this set . Thus Corollary 9.9 shows that p vanishes on σ ( A ) , which means that = Ф 0 . To prove ( 76 ) it is seen from Theorem 9.3 ...
Page 2046
... vanishes for 1 on the positive real axis . Thus ƒ1 ( 51 ) = 0 for ( 1 ) > 0 . Thus for R ( 1 ) > 0 the function ― ƒ2 ( 52 ) = [ S ( $ 1 + ( 2 ) — S ( 51 ) S ( $ 2 ) ] ❤ vanishes for 2 on the positive real axis and hence ƒ2 ( 52 ) = 0 ...
... vanishes for 1 on the positive real axis . Thus ƒ1 ( 51 ) = 0 for ( 1 ) > 0 . Thus for R ( 1 ) > 0 the function ― ƒ2 ( 52 ) = [ S ( $ 1 + ( 2 ) — S ( 51 ) S ( $ 2 ) ] ❤ vanishes for 2 on the positive real axis and hence ƒ2 ( 52 ) = 0 ...
Page 2161
... vanishes on the manifold ( i ) . Let x * be such a functional . Then ( ii ) ( λ 。 I * — T * ) 1x * = 0 . To see that x * 0 it will first be shown that ( iii ) = - x * € ( λ 。 I * — T * ) ŊX * . 0 If ( iii ) is not true , then , since ...
... vanishes on the manifold ( i ) . Let x * be such a functional . Then ( ii ) ( λ 。 I * — T * ) 1x * = 0 . To see that x * 0 it will first be shown that ( iii ) = - x * € ( λ 。 I * — T * ) ŊX * . 0 If ( iii ) is not true , then , since ...
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