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 1930
... plane which contains the void set and the whole plane , in short , if Σ is a field of sets in the complex plane , then a spectral measure E on Σ is called a resolution of the identity ( or a spectral resolution ) for the operator T if E ...
... plane which contains the void set and the whole plane , in short , if Σ is a field of sets in the complex plane , then a spectral measure E on Σ is called a resolution of the identity ( or a spectral resolution ) for the operator T if E ...
Page 2043
... plane in the imaginary axis also hold . PROOF . We shall first need a bound for the norm of the analytic extension T1 ( ) of the semi - group T ( t ) to the half plane R ( ) > 0 . Let R ( ) > 0 so that ete with π / 20 / 2 . Then since ...
... plane in the imaginary axis also hold . PROOF . We shall first need a bound for the norm of the analytic extension T1 ( ) of the semi - group T ( t ) to the half plane R ( ) > 0 . Let R ( ) > 0 so that ete with π / 20 / 2 . Then since ...
Page 2087
... plane R ( Č ) > 0 . For every ( 0 ) in Ho there is one and only one continuous map t → q ( t ) of [ 0 , ∞ ) into HP which is differentiable for t > 0 and has the properties ( ii ) ( iii ) ( iv ) p ( t ) e ( p ) T ( 24 ) ( RN ) , g ...
... plane R ( Č ) > 0 . For every ( 0 ) in Ho there is one and only one continuous map t → q ( t ) of [ 0 , ∞ ) into HP which is differentiable for t > 0 and has the properties ( ii ) ( iii ) ( iv ) p ( t ) e ( p ) T ( 24 ) ( RN ) , g ...
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