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 on an open set D ( f ) ≥ p ( T ) and such that ( §I — T ) ƒ ( § ) = x , It is clear that , for such an extension , ƒ ( § ) = R ( § ; T ) x , έe D ( f ) . ξερ ( Τ ) . The notion of " analytic extension " differs from that of " ...
... analytic on an open set D ( f ) ≥ p ( T ) and such that ( §I — T ) ƒ ( § ) = x , It is clear that , for such an extension , ƒ ( § ) = R ( § ; T ) x , έe D ( f ) . ξερ ( Τ ) . The notion of " analytic extension " differs from that of " ...
Page 1932
... analytic function with domain p ( x ) and with x ( ) = R ( ¿ ; 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 ( ¿ ; 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 ) ...
... 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 ) ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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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