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 2214
... weakly complete space . Then an operator is in the weakly closed algebra generated by B if and only if it leaves invariant every closed linear manifold which is invariant under every member of B. PROOF . It was observed in the preceding ...
... weakly complete space . Then an operator is in the weakly closed algebra generated by B if and only if it leaves invariant every closed linear manifold which is invariant under every member of B. PROOF . It was observed in the preceding ...
Page 2217
... weakly closed operator algebra generated by a o - complete Boolean algebra B of projections in a B - space if and only if it leaves invariant every closed linear manifold which remains invariant under every element of B. PROOF . Let B1 ...
... weakly closed operator algebra generated by a o - complete Boolean algebra B of projections in a B - space if and only if it leaves invariant every closed linear manifold which remains invariant under every element of B. PROOF . Let B1 ...
Page 2218
... weakly closed operator algebra generated by B ) is the same as the uniformly closed operator algebra generated by B1 . Every operator in such a uniformly closed algebra is , by Lemma 9 , given in terms of a countably additive spectral ...
... weakly closed operator algebra generated by B ) is the same as the uniformly closed operator algebra generated by B1 . Every operator in such a uniformly closed algebra is , by Lemma 9 , given in terms of a countably additive spectral ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
Copyright | |
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Common terms and phrases
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