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 1986
... establish the inversion formula ( 5 ) . Once this is done , it will follow that F is one - to - one on Ø and that q ( s ) = ( F2q ) ( − s ) , which proves that FØ = Ø and thus that the ... established by 1986 XV.11.1 XV . SPECTRAL OPERATORS.
... establish the inversion formula ( 5 ) . Once this is done , it will follow that F is one - to - one on Ø and that q ( s ) = ( F2q ) ( − s ) , which proves that FØ = Ø and thus that the ... established by 1986 XV.11.1 XV . SPECTRAL OPERATORS.
Page 2182
... established , the final assertion concerning the nature of A ( B ) will follow from Lemma 1 together with the remarks in the paragraph preceding the statement of the theorem . The first part of the theorem will be established by ...
... established , the final assertion concerning the nature of A ( B ) will follow from Lemma 1 together with the remarks in the paragraph preceding the statement of the theorem . The first part of the theorem will be established by ...
Page 2212
... establish the equation ( viii ) fFi = f1Xo ( F ) , FEB . To prove this , let g = fX ( F ) so that , using ( vii ) , we ... established . Hence we may and shall assume , in the proof of ( ix ) , that I on σ2 = Since A ( xy ) = Ax- Ay it ...
... establish the equation ( viii ) fFi = f1Xo ( F ) , FEB . To prove this , let g = fX ( F ) so that , using ( vii ) , we ... established . Hence we may and shall assume , in the proof of ( ix ) , that I on σ2 = Since A ( xy ) = Ax- Ay it ...
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