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 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ 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