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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Results 1-3 of 85
Page 1956
... follows from Theorem 2 that = is in the point spectrum of T. If E ( { } ) = 0 then it follows from Theorem 2 that IT is one - to - one . By Corollary 7.12 the set ( ÀI — T ) X is dense in X and hence is in the continuous spectrum of ...
... follows from Theorem 2 that = is in the point spectrum of T. If E ( { } ) = 0 then it follows from Theorem 2 that IT is one - to - one . By Corollary 7.12 the set ( ÀI — T ) X is dense in X and hence is in the continuous spectrum of ...
Page 2246
... follows that R ( A ) is a bounded operator whose range is contained in the domain of C. It is clear then that ( AIC ) R ( A ) x = x for x in H and R ( X ) ( λ — C ) x x for x in D ( C ) , so that R ( A ) = R ( A ; C ) and λ σ ( C ) . On ...
... follows that R ( A ) is a bounded operator whose range is contained in the domain of C. It is clear then that ( AIC ) R ( A ) x = x for x in H and R ( X ) ( λ — C ) x x for x in D ( C ) , so that R ( A ) = R ( A ; C ) and λ σ ( C ) . On ...
Page 2437
... follows that So S. Moreover , the operator S is plainly symmetric , so that it follows from Corollary XII.4.13 ( b ) that S is self adjoint . Since So WT , W - 1S , while So S , it follows by Lemma XII.4.8 ( a ) , and using the fact ...
... follows that So S. Moreover , the operator S is plainly symmetric , so that it follows from Corollary XII.4.13 ( b ) that S is self adjoint . Since So WT , W - 1S , while So S , it follows by Lemma XII.4.8 ( a ) , and using the fact ...
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