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 1931
... analytic extension of R ( § ; T ) x will be meant an X - valued function f defined and analytic on an open set D ( ƒ ) ≥ p ( T ) and such that It is clear that , for such an extension , ( §I — T ) ƒ ( § ) = x , έ = D ( f ) . ξερ ( Τ ) ...
... analytic extension of R ( § ; T ) x will be meant an X - valued function f defined and analytic on an open set D ( ƒ ) ≥ p ( T ) and such that It is clear that , for such an extension , ( §I — T ) ƒ ( § ) = x , έ = D ( f ) . ξερ ( Τ ) ...
Page 1932
... analytic function with domain p ( x ) and with x ( ) = R ( E ; T ) x , ξερ ( Τ ) . It will be shown in the next section that , if T is a spectral operator , the function R ( § ; T ) x has , for every x in X , the single valued extension ...
... analytic function with domain p ( x ) and with x ( ) = R ( E ; T ) x , ξερ ( Τ ) . It will be shown in the next section that , if T is a spectral operator , the function R ( § ; T ) x has , for every x in X , the single valued extension ...
Page 2248
... analytic in a domain U which , when taken together with a finite number of exceptional points p , includes a ... analytic at infinity , then e1 = f - 1 ( e ) is bounded , and it follows from Theorem 9 ( ii ) that D ( f ( T ) ) E ( e1 ) X ...
... analytic in a domain U which , when taken together with a finite number of exceptional points p , includes a ... analytic at infinity , then e1 = f - 1 ( e ) is bounded , and it follows from Theorem 9 ( ii ) that D ( f ( T ) ) E ( e1 ) X ...
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