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 1917
... limit 1 U = lim ettr'e - itT . This purely formal argument inspires us to study the limit appearing above , and indeed it develops that if the difference TT satisfies suitable hypotheses , this limit will exist in the strong topology ...
... limit 1 U = lim ettr'e - itT . This purely formal argument inspires us to study the limit appearing above , and indeed it develops that if the difference TT satisfies suitable hypotheses , this limit will exist in the strong topology ...
Page 2219
... Limits of Spectral Operators : Non - Commutative Case In this section conditions will be given to insure that the strong limit T = lim T of a generalized sequence { T } of scalar type spectral opera- tors is itself a scalar type ...
... Limits of Spectral Operators : Non - Commutative Case In this section conditions will be given to insure that the strong limit T = lim T of a generalized sequence { T } of scalar type spectral opera- tors is itself a scalar type ...
Page 2454
... limit Uv for all v in Hilbert space . However , by adding suitable hypo- theses and by arguing more carefully , we ... limit as t → ∞ if and only if ( 3.2 ) x ' has a limit as t∞ , and that , if either limit exists , both limits are ...
... limit Uv for all v in Hilbert space . However , by adding suitable hypo- theses and by arguing more carefully , we ... limit as t → ∞ if and only if ( 3.2 ) x ' has a limit as t∞ , and that , if either limit exists , both limits are ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra 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 denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero