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 2217
... limit lim , Ex does not exist . Let X ( x ) , X1 ( x ) be the closed linear manifolds generated by the sets { ExE ... limit lim , Eax does not exist , the limit lim , E fails to exist in the strong topology . It follows from Lemma 4 that ...
... limit lim , Ex does not exist . Let X ( x ) , X1 ( x ) be the closed linear manifolds generated by the sets { ExE ... limit lim , Eax does not exist , the limit lim , E fails to exist in the strong topology . It follows from Lemma 4 that ...
Page 2219
... Limits of Spectral Operators : Non - Commutative Case Q.E.D. In this section conditions will be given to insure that the strong limit T = lim Ta of a generalized sequence { T } of scalar type spectral opera- tors is itself a scalar type ...
... Limits of Spectral Operators : Non - Commutative Case Q.E.D. In this section conditions will be given to insure that the strong limit T = lim Ta of a generalized sequence { T } of scalar type spectral opera- tors is itself a scalar type ...
Page 2484
... limit on the left and the proper value integral on the right existing almost everywhere . 11 ( Friedrichs ' Identity ) ... limit integral + + ∞0 lim ( A ( s , σ ) B ( o , t ) do , + 0 + 3 o - tie -∞ and I. ( A ) B for the limit integral ...
... limit on the left and the proper value integral on the right existing almost everywhere . 11 ( Friedrichs ' Identity ) ... limit integral + + ∞0 lim ( A ( s , σ ) B ( o , t ) do , + 0 + 3 o - tie -∞ and I. ( A ) B for the limit integral ...
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