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 1945
... weak product topology so that , by definition , the sets { ƒ | ƒ € L , \ f ( x , y ) − g ( x , y ) | < ε } , where x , ye H and ɛ > 0 , form a subbase for the neighborhoods of a point g in 2. It is easily seen that P is a closed set in ...
... weak product topology so that , by definition , the sets { ƒ | ƒ € L , \ f ( x , y ) − g ( x , y ) | < ε } , where x , ye H and ɛ > 0 , form a subbase for the neighborhoods of a point g in 2. It is easily seen that P is a closed set in ...
Page 2160
... weak topology , we have lim ( no ) R ( λn ; T ) x = y . n Then ( IT ) y is the weak limit of ( λn — λo ) ( λ 。 I — T ) R ( λn ; T ) x = ( λn — do ) x — ( λo — λn ) 2R ( λn ; T ) x , and this limit is clearly zero . Thus ( AIT ) y = 0 ...
... weak topology , we have lim ( no ) R ( λn ; T ) x = y . n Then ( IT ) y is the weak limit of ( λn — λo ) ( λ 。 I — T ) R ( λn ; T ) x = ( λn — do ) x — ( λo — λn ) 2R ( λn ; T ) x , and this limit is clearly zero . Thus ( AIT ) y = 0 ...
Page 2281
... topologies and also when X * has its X - topology and Σî = 1 L1 ( A , B , v1 ) has its weak topology . PROOF . Most of the proof of this theorem is a straightforward modi- fication of the proof of Theorem 19. Given x * € X * there exist ...
... topologies and also when X * has its X - topology and Σî = 1 L1 ( A , B , v1 ) has its weak topology . PROOF . Most of the proof of this theorem is a straightforward modi- fication of the proof of Theorem 19. Given x * € X * there exist ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
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