Linear Operators: Spectral operators |
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Page 2154
... manifolds { x | ( T — \ I ) TM x = 0 } increase with m , it follows that - ( T_AI ) n + 1 ¥ + { x | ( T_ \ I ) n + 1 = 0 } is dense in X. By induction , it is seen that the manifold - ( T − \ I ) n + kX + { x | ( T − λI ) n + kx = 0 } ...
... manifolds { x | ( T — \ I ) TM x = 0 } increase with m , it follows that - ( T_AI ) n + 1 ¥ + { x | ( T_ \ I ) n + 1 = 0 } is dense in X. By induction , it is seen that the manifold - ( T − \ I ) n + kX + { x | ( T − λI ) n + kx = 0 } ...
Page 2214
... manifold which is invariant under every member of B. The theorem shows that A is in the uniformly closed algebra ( B ) generated by B. Thus W ( B ) ≤ A ( B ) . On the other hand , it is clear that A ( B ) ≤ W ( B ) . Q.E.D. The ...
... manifold which is invariant under every member of B. The theorem shows that A is in the uniformly closed algebra ( B ) generated by B. Thus W ( B ) ≤ A ( B ) . On the other hand , it is clear that A ( B ) ≤ W ( B ) . Q.E.D. The ...
Page 2217
... manifold which remains invariant under every element of B. 1 PROOF . Let B1 be the strong closure of B. By Lemma 23 ... manifold that is left invariant by every member of B. Since it is evident that a closed linear manifold is invariant ...
... manifold which remains invariant under every element of B. 1 PROOF . Let B1 be the strong closure of B. By Lemma 23 ... manifold that is left invariant by every member of B. Since it is evident that a closed linear manifold is invariant ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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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