Linear Operators: Spectral operators |
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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. 1 PROOF . It was observed in the ...
... 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. 1 PROOF . It was observed in the ...
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. 1 PROOF . Let ...
... 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. 1 PROOF . Let ...
Page 2218
... weakly closed operator algebra generated by a spectral operator of scalar type and the projections in its resolu- tion of the identity is a spectral operator of scalar type . PROOF . Since a spectral operator of scalar type is clearly ...
... weakly closed operator algebra generated by a spectral operator of scalar type and the projections in its resolu- tion of the identity is a spectral operator of scalar type . PROOF . Since a spectral operator of scalar type is clearly ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero